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Journal articles on the topic 'Nonlinear parabolic and elliptic boundary values problems'

Author: Grafiati

Published: 10 March 2023

Last updated: 11 March 2023

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1

Hamamuki, Nao, and Qing Liu. "A deterministic game interpretation for fully nonlinear parabolic equations with dynamic boundary conditions." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 13. http://dx.doi.org/10.1051/cocv/2019076.

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This paper is devoted to deterministic discrete game-theoretic interpretations for fully nonlinear parabolic and elliptic equations with nonlinear dynamic boundary conditions. It is known that the classical Neumann boundary condition for general parabolic or elliptic equations can be generated by including reflections on the boundary to the interior optimal control or game interpretations. We study a dynamic version of such type of boundary problems, generalizing the discrete game-theoretic approach proposed by Kohn-Serfaty (2006, 2010) for Cauchy problems and later developed by Giga-Liu (2009

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2

Shangbin, Cui. "Some comparison and uniqueness theorems for nonlinear elliptic boundary value problems and nonlinear parabolic initial-boundary value problems." Nonlinear Analysis: Theory, Methods & Applications 29, no. 9 (1997): 1079–90. http://dx.doi.org/10.1016/s0362-546x(96)00097-1.

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3

Chow, S. S., and R. D. Lazarov. "Superconvergence analysis of flux computations for nonlinear problems." Bulletin of the Australian Mathematical Society 40, no. 3 (1989): 465–79. http://dx.doi.org/10.1017/s0004972700017536.

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In this paper we consider the error estimates for some boundary-flux calculation procedures applied to two-point semilinear and strongly nonlinear elliptic boundary value problems. The case of semilinear parabolic problems is also studied. We prove that the computed flux is superconvergent with second and third order of convergence for linear and quadratic elements respectively. Corresponding estimates for higher order elements may also be obtained by following the general line of argument.

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4

SHAKHMUROV, VELI B., and AIDA SAHMUROVA. "Mixed problems for degenerate abstract parabolic equations and applications." Carpathian Journal of Mathematics 34, no. 2 (2018): 247–54. http://dx.doi.org/10.37193/cjm.2018.02.13.

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Degenerate abstract parabolic equations with variable coefficients are studied. Here the boundary conditions are nonlocal. The maximal regularity properties of solutions for elliptic and parabolic problems and Strichartz type estimates in mixed Lebesgue spaces are obtained. Moreover, the existence and uniqueness of optimal regular solution of mixed problem for nonlinear parabolic equation is established. Note that, these problems arise in fluid mechanics and environmental engineering.

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5

Gavrilyuk, I. P. "Approximation of the Operator Exponential and Applications." Computational Methods in Applied Mathematics 7, no. 4 (2007): 294–320. http://dx.doi.org/10.2478/cmam-2007-0019.

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AbstractA review of the exponentially convergent approximations to the operator exponential is given. The applications to inhomogeneous parabolic and elliptic equations, nonlinear parabolic equations, tensor-product approximations of multidimensional solution operators as well as to parabolic problems with time dependent coefficients and boundary conditions are discussed.

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6

Indrei, Emanuel, and Andreas Minne. "Regularity of solutions to fully nonlinear elliptic and parabolic free boundary problems." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 33, no. 5 (2016): 1259–77. http://dx.doi.org/10.1016/j.anihpc.2015.03.009.

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7

I. Vishik, Mark, and Sergey Zelik. "Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit." Communications on Pure & Applied Analysis 13, no. 5 (2014): 2059–93. http://dx.doi.org/10.3934/cpaa.2014.13.2059.

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8

Zhang, Qi S. "A general blow-up result on nonlinear boundary-value problems on exterior domains." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 2 (2001): 451–75. http://dx.doi.org/10.1017/s0308210500000950.

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In the first part, we study several exterior boundary-value problems covering three types of semilinear equations: elliptic, parabolic and hyperbolic. By a unified approach, we show that these problems share a common critical behaviour. In the second part we prove a blow-up result for an inhomogeneous porous medium equation with the critical exponent, which was left open in a previous paper.

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9

Andreu, F., N. Igbida, J. M. Mazón, and J. Toledo. "Renormalized solutions for degenerate elliptic–parabolic problems with nonlinear dynamical boundary conditions and L1-data." Journal of Differential Equations 244, no. 11 (2008): 2764–803. http://dx.doi.org/10.1016/j.jde.2008.02.022.

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10

Galkowski, Jeffrey. "Pseudospectra of semiclassical boundary value problems." Journal of the Institute of Mathematics of Jussieu 14, no. 2 (2014): 405–49. http://dx.doi.org/10.1017/s1474748014000061.

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AbstractWe consider operators$ - \Delta + X $, where$ X $is a constant vector field, in a bounded domain, and show spectral instability when the domain is expanded by scaling. More generally, we consider semiclassical elliptic boundary value problems which exhibit spectral instability for small values of the semiclassical parameter$h$, which should be thought of as the reciprocal of the Péclet constant. This instability is due to the presence of the boundary: just as in the case of$ - \Delta + X $, some of our operators are normal when considered on$\mathbb{R}^d$. We characterize the semiclass

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11

Lipitakis, Anastasia-Dimitra. "The Numerical Solution of Singularly Perturbed Nonlinear Partial Differential Equations in Three Space Variables: The Adaptive Explicit Inverse Preconditioning Approach." Modelling and Simulation in Engineering 2019 (January 2, 2019): 1–9. http://dx.doi.org/10.1155/2019/5157145.

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Critical comments on the complexity of computational systems and the basic singularly perturbed (SP) concepts are given. A class of several complex SP nonlinear elliptic equations arising in various branches of science, technology, and engineering is presented. A classification of complex SP nonlinear PDEs with characteristic boundary value problems is described. A modified explicit preconditioned conjugate gradient method based on explicit inverse preconditioners is presented. The numerical solution of a characteristic 3D SP nonlinear parabolic model is analytically given and numerical result

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12

Rihova-Skabrahova, Dana. "Linear Scheme for Finite Element Solution of Nonlinear Parabolic-Elliptic Problems with Nonhomogeneous Dirichlet Boundary Condition." Applications of Mathematics 46, no. 2 (2001): 103–44. http://dx.doi.org/10.1023/a:1013783722140.

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13

Lieberman, Gary A. "On The Hölder Gradient Estimate For Solutions Of Nonlinear Elliptic And Parabolic Oblique Boundary Value Problems." Communications in Partial Differential Equations 15, no. 4 (1990): 515–23. http://dx.doi.org/10.1080/03605309908820696.

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14

Nefedov, N. N. "Development of Methods of Asymptotic Analysis of Transition Layers in Reaction–Diffusion–Advection Equations: Theory and Applications." Computational Mathematics and Mathematical Physics 61, no. 12 (2021): 2068–87. http://dx.doi.org/10.1134/s0965542521120095.

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Abstract This work presents a review and analysis of modern asymptotic methods for analysis of singularly perturbed problems with interior and boundary layers. The central part of the work is a review of the work of the author and his colleagues and disciples. It highlights boundary and initial-boundary value problems for nonlinear elliptic and parabolic partial differential equations, as well as periodic parabolic problems, which are widely used in applications and are called reaction–diffusion and reaction–diffusion–advection equations. These problems can be interpreted as models in chemical

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15

Zhang, Junjie, Shenzhou Zheng, and Chunyan Zuo. "$ W^{2, p} $-regularity for asymptotically regular fully nonlinear elliptic and parabolic equations with oblique boundary values." Discrete & Continuous Dynamical Systems - S 14, no. 9 (2021): 3305. http://dx.doi.org/10.3934/dcdss.2021080.

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<p style='text-indent:20px;'>We prove a global <inline-formula><tex-math id="M1">\begin{document}$ W^{2, p} $\end{document}</tex-math></inline-formula>-estimate for the viscosity solution to fully nonlinear elliptic equations <inline-formula><tex-math id="M2">\begin{document}$ F(x, u, Du, D^{2}u) = f(x) $\end{document}</tex-math></inline-formula> with oblique boundary condition in a bounded <inline-formula><tex-math id="M3">\begin{document}$ C^{2, \alpha} $\end{document}</tex-math></inline-formula>-domain for every &

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16

Gwinner, J. "Three-Field Modelling of Nonlinear Nonsmooth Boundary Value Problems and Stability of Differential Mixed Variational Inequalities." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/108043.

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The purpose of this paper is twofold. Firstly we consider nonlinear nonsmooth elliptic boundary value problems, and also related parabolic initial boundary value problems that model in a simplified way steady-state unilateral contact with Tresca friction in solid mechanics, respectively, stem from nonlinear transient heat conduction with unilateral boundary conditions. Here a recent duality approach, that augments the classical Babuška-Brezzi saddle point formulation for mixed variational problems to twofold saddle point formulations, is extended to the nonsmooth problems under consideration.

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17

Abdullayev, Akmaljon, Kholsaid Kholturayev, and Nigora Safarbayeva. "Exact method to solve of linear heat transfer problems." E3S Web of Conferences 264 (2021): 02059. http://dx.doi.org/10.1051/e3sconf/202126402059.

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When approximating multidimensional partial differential equations, the values of the grid functions from neighboring layers are taken from the previous time layer or approximation. As a result, along with the approximation discrepancy, an additional discrepancy of the numerical solution is formed. To reduce this discrepancy when solving a stationary elliptic equation, parabolization is carried out, and the resulting equation is solved by the method of successive approximations. This discrepancy is eliminated in the approximate analytical method proposed below for solving two-dimensional equat

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18

KASCHENKO, S. A. "BIFURCATIONAL FEATURES IN SYSTEMS OF NONLINEAR PARABOLIC EQUATIONS WITH WEAK DIFFUSION." International Journal of Bifurcation and Chaos 15, no. 11 (2005): 3595–606. http://dx.doi.org/10.1142/s0218127405014258.

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Asymptotic solutions of parabolic boundary value problems are studied in a neighborhood of both an equilibrium state and a cycle in near-critical cases which can be considered as infinite-dimensional due to small values of the diffusion coefficients. Algorithms are developed to construct normalized equations in such situations. Principle difference between bifurcations in two-dimensional and one-dimensional spatial systems is demonstrated.

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19

Da Silva, Edcarlos Domingos, and Francisco Odair De Paiva. "Landesman-lazer type conditions and multiplicity results for nonlinear elliptic problems with neumann boundary values." Acta Mathematica Sinica, English Series 30, no. 2 (2014): 229–50. http://dx.doi.org/10.1007/s10114-014-2750-2.

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20

Koshanov, B. D., N. Kakharman, R. U. Segizbayeva, and Zh B. Sultangaziyeva. "Two theorems on estimates for solutions of one class of nonlinear equations in a finite-dimensional space." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 107, no. 3 (2022): 70–84. http://dx.doi.org/10.31489/2022m3/70-84.

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The need to study boundary value problems for elliptic parabolic equations is dictated by numerous practical applications in the theoretical study of the processes of hydrodynamics, electrostatics, mechanics, heat conduction, elasticity theory and quantum physics. In this paper, we obtain two theorems on a priori estimates for solutions of nonlinear equations in a finite-dimensional Hilbert space. The work consists of four items. In the first subsection, the notation used and the statement of the main results are given. In the second subsection, the main lemmas are given. The third section is

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21

Shan, Maria. "Keller-Osserman a priori estimates for doubly nonlinear anisotropic parabolic equations with absorption term." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 32 (December 28, 2018): 149–59. http://dx.doi.org/10.37069/1683-4720-2018-32-15.

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We are concerned with divergence type quasilinear parabolic equation with measurable coefficients and lower order terms model of which is a doubly nonlinear anisotropic parabolic equations with absorption term. This class of equations has numerous applications which appear in modeling of electrorheological fluids, image precessing, theory of elasticity, theory of non-Newtonian fluids with viscosity depending on the temperature. But the qualitative theory doesn't construct for these anisotropic equations. So, naturally, that during the last decade there has been growing substantial development

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22

Nkashama, M. N., and S. B. Robinson. "Resonance and non-resonance in terms of average values. II." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 5 (2001): 1217–35. http://dx.doi.org/10.1017/s0308210500001359.

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We prove existence results for semilinear elliptic boundary-value problems in both the resonance and non-resonance cases. What sets our results apart is that we impose sufficient conditions for solvability in terms of the (asymptotic) average values of the nonlinearities, thus allowing the nonlinear term to have significant oscillations outside the given spectral gap as long as it remains within the interval on the average in some sense. This work generalizes the results of a previous paper, which dealt exclusively with the ordinary differential equation (ODE) case and relied on ODE techniques

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23

Bokalo, Mykola, Oleh Buhrii, and Nikolyetta Hryadil. "Initial–boundary value problems for nonlinear elliptic–parabolic equations with variable exponents of nonlinearity in unbounded domains without conditions at infinity." Nonlinear Analysis 192 (March 2020): 111700. http://dx.doi.org/10.1016/j.na.2019.111700.

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24

Warma, Mahamadi. "Regularity and well-posedness of some quasi-linear elliptic and parabolic problems with nonlinear general Wentzell boundary conditions on nonsmooth domains." Nonlinear Analysis: Theory, Methods & Applications 75, no. 14 (2012): 5561–88. http://dx.doi.org/10.1016/j.na.2012.05.004.

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25

Turkyilmazoglu, Mustafa. "Solution of Initial and Boundary Value Problems by an Effective Accurate Method." International Journal of Computational Methods 14, no. 06 (2017): 1750069. http://dx.doi.org/10.1142/s0219876217500694.

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The newly proposed analytic approximate solution method in the recent publications [Turkyilmazoglu, M. [2013] “Effective computation of exact and analytic approximate solutions to singular nonlinear equations of Lane-Emden-Fowler type,” Appl. Math. Mod. 37, 7539–7548; Turkyilmazoglu, M. [2014] “An effective approach for numerical solutions of high-order Fredholm integro-differential equations,” Appl. Math. Comput. 227, 384–398; Turkyilmazoglu, M. [2015] “Parabolic partial differential equations with nonlocal initial and boundary values,” Int. J. Comput. Methods, doi: 10.1142/S0219876215500243]

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26

Devaud, Denis. "Petrov–Galerkin space-time hp-approximation of parabolic equations in H1/2." IMA Journal of Numerical Analysis 40, no. 4 (2019): 2717–45. http://dx.doi.org/10.1093/imanum/drz036.

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Abstract We analyse a class of variational space-time discretizations for a broad class of initial boundary value problems for linear, parabolic evolution equations. The space-time variational formulation is based on fractional Sobolev spaces of order $1/2$ and the Riemann–Liouville derivative of order $1/2$ with respect to the temporal variable. It accommodates general, conforming space discretizations and naturally accommodates discretization of infinite horizon evolution problems. We prove an inf-sup condition for $hp$-time semidiscretizations with an explicit expression of stable test func

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27

ANDREU, FUENSANTA, JOSÉ M. MAZÓN, and MIRCEA SOFONEA. "ENTROPY SOLUTIONS IN THE STUDY OF ANTIPLANE SHEAR DEFORMATIONS FOR ELASTIC SOLIDS." Mathematical Models and Methods in Applied Sciences 10, no. 01 (2000): 99–126. http://dx.doi.org/10.1142/s0218202500000082.

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The concept of entropy solution was recently introduced in the study of Dirichlet problems for elliptic equations and extended for parabolic equations with nonlinear boundary conditions. The aim of this paper is to use the method of entropy solutions in the study of a new problem which arise in the theory of elasticity. More precisely, we consider here the infinitesimal antiplane shear deformation of a cylindrical elastic body subjected to given forces and in a frictional contact with a rigid foundation. The elastic constitutive law is physically nonlinear and the friction is described by a st

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28

Vyas, Prashant Dineshbhai, Harish C. Thakur, and Veera P. Darji. "Nonlinear analysis of convective-radiative longitudinal fin of various profiles." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 6 (2019): 3065–82. http://dx.doi.org/10.1108/hff-08-2018-0444.

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Purpose This paper aims to study nonlinear heat transfer through a longitudinal fin of three different profiles. Design/methodology/approach A truly meshfree method is used to undertake a nonlinear analysis to predict temperature distribution and heat-transfer rate. Findings A longitudinal fin of three different profiles, such as rectangular, triangular and concave parabolic, are analyzed. Temperature variation, along with the fin length and rate of heat transfer in steady state, under convective and convective-radiative environments has been demonstrated and explained. Moving least square (ML

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29

Teirumnieka, Ērika, Ilmārs Kangro, Edmunds Teirumnieks, and Harijs Kalis. "The analytical solution of the 3D model with Robin's boundary conditions for 2 peat layers." Environment. Technology. Resources. Proceedings of the International Scientific and Practical Conference 3 (June 16, 2015): 186. http://dx.doi.org/10.17770/etr2015vol3.618.

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<p>In this paper we consider averaging methods for solving the 3-D boundary value problem in domain containing 2 layers of the peat block. We consider the metal concentration in the peat blocks. Using experimental data the mathematical model for calculation of concentration of metal in different points in every peat layer is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for elliptic type partial differential equations of second order with piece-wise diffusion coefficients in every direction and peat layers.</p><p

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30

Rotko, V. V. "INVERSE PROBLEMS FOR MATHEMATICAL MODELS WITH THE POINTWISE OVERDETERMINATION." Yugra State University Bulletin 14, no. 3 (2018): 57–66. http://dx.doi.org/10.17816/byusu2018057-66.

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In the article we examine well-posedness questions in the Sobolev spaces of an inverse source problem in the case of a quasilinear parabolic system of the second order. These problem arise when describing heat and mass transfer, diffusion, filtration, and in many other fields. The main part of the operator is linear. The unknowns occur in the nonlinear right-hand side. In particular, this class of problems includes the coefficient inverse problems on determinations of the lower order coefficients in a parabolic equation or a system. The overdetermination conditions are the values of a solution

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31

Crochet, Marcel J. "Numerical Simulation of Viscoelastic Flow: A Review." Rubber Chemistry and Technology 62, no. 3 (1989): 426–55. http://dx.doi.org/10.5254/1.3536253.

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Abstract It is evident that a major effort has been accomplished over the last ten years toward the development of numerical methods for solving viscoelatic flow. The problem was clearly much harder than expected. Several extensive reviews have been devoted to a detailed account of the difficulties encountered in reaching moderate values of the Weissenberg number. The numerical and analytical work undertaken in parallel by several research groups has led to some important conclusions which paved the way for recent promising development. First, numerical algorithms for solving highly nonlinear

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32

Sumin, Vladimir I. "Volterra funktional equations in the stability problem for the existence of global solutions of distributed controlled systems." Russian Universities Reports. Mathematics, no. 132 (2020): 422–40. http://dx.doi.org/10.20310/2686-9667-2020-25-132-422-440.

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Earlier the author proposed a rather general form of describing controlled initial–boundary value problems (CIBVPs) by means of Volterra functional equations (VFE) z(t)=f(t,A[z](t),v(t) ), t≡{t^1,⋯,t^n }∈Π⊂R^n, z∈L_p^m≡(L_p (Π) )^m, where f(.,.,.):Π×R^l×R^s→R^m; v(.)∈D⊂L_k^s – control function; A:L_p^m (Π)→L_q^l (Π)- linear operator; the operator A is a Volterra operator for some system T of subsets of the set Π in the following sense: for any H∈T, the restriction A├ [z]┤|_H does not depend on the values of ├ z┤|_(Π\H); (this definition of the Volterra operator is a direct multidimensional gen

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33

Berselli, Luigi C., and Michael Růžička. "Space–time discretization for nonlinear parabolic systems with p-structure." IMA Journal of Numerical Analysis, December 23, 2020. http://dx.doi.org/10.1093/imanum/draa079.

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Abstract In this paper we consider nonlinear parabolic systems with elliptic part, depending only on the symmetric gradient, which can be also degenerate. We prove optimal error estimates for solutions with natural regularity. The main novelty, with respect to previous results, is that we obtain the estimates directly without introducing intermediate semidiscrete problems, which enables the treatment of homogeneous Dirichlet boundary conditions. In addition, we prove the existence of solutions of the continuous problem with the requested regularity, if the data of the problem are smooth enough

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34

Dancer, E. N. "Stable and Finite Morse Index Solutions for Dirichlet Problems with Small Diffusion in a Degenerate Case and Problems with Infinite Boundary Values." Advanced Nonlinear Studies 9, no. 4 (2009). http://dx.doi.org/10.1515/ans-2009-0405.

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AbstractWe consider weakly nonlinear elliptic equations with small diffusion in the case where the nonlinearity has a non-nodal zero. We show that there is an unexpected connection with problems with infinite boundary values.

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35

Yang, Guangchong, and Yanqiu Chen. "Nonnegative Solutions of a Nonlinear System and Applications to Elliptic BVPs*." Journal of Applied Mathematics & Bioinformatics, August 31, 2021, 15–26. http://dx.doi.org/10.47260/jamb/1122.

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Abstract In this communication, we study the existence of nonnegative solutions of a nonlinear system in Banach spaces. These maps involved in the system defined on cone do not necessarily take values in the cone. Using fixed point theorems just established for this type of mappings, nonnegative solutions of the system are obtained and used to investigate elliptic boundary value problems (BVPs). MSC(2010): 47H10, 35J57. Keywords: Nonlinear system, Nonnegative solutions, Nowhere normal-outward maps, Fixed point, Elliptic BVPs.

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36

Balázsová, Monika, Miloslav Feistauer, and Anna-Margarete Sändig. "Regularity results and numerical solution by the discontinuous Galerkin method to semilinear parabolic initial boundary value problems with nonlinear Newton boundary conditions in a polygonal space-time cylinder." Journal of Numerical Mathematics, June 25, 2022. http://dx.doi.org/10.1515/jnma-2021-0113.

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Abstract In this note we consider a parabolic evolution equation in a polygonal space-time cylinder. We show, that the elliptic part is given by a m-accretive mapping from L q (Ω) → L q (Ω). Therefore we can apply the theory of nonlinear semigroups in Banach spaces in order to get regularity results in time and space. The second part of the paper deals with the numerical solution of the problem. It is dedicated to the application of the space-time discontinuous Galerkin method (STDGM). It means that both in space as well as in time discontinuous piecewise polynomial approximations of the solut

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37

Baraket, Sami, and Vicenţiu D. Rădulescu. "Combined Effects of Concave-Convex Nonlinearities in a Fourth-Order Problem with Variable Exponent." Advanced Nonlinear Studies 16, no. 3 (2016). http://dx.doi.org/10.1515/ans-2015-5032.

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AbstractWe study two classes of nonhomogeneous elliptic problems with Dirichlet boundary condition and involving a fourth-order differential operator with variable exponent and power-type nonlinearities. The first result of this paper establishes the existence of a nontrivial weak solution in the case of a small perturbation of the right-hand side. The proof combines variational methods, including the Ekeland variational principle and the mountain pass theorem of Ambrosetti and Rabinowitz. Next we consider a very related eigenvalue problem and we prove the existence of nontrivial weak solution

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38

Baber, Muhammad Z., Aly R. Seadway, Nauman Ahmed, Muhammad S. Iqbal, and Muhammad W. Yasin. "Selection of solitons coinciding the numerical solutions for uniquely solvable physical problems: A comparative study for the nonlinear stochastic Gross–Pitaevskii equation in dispersive media." International Journal of Modern Physics B, December 21, 2022. http://dx.doi.org/10.1142/s0217979223501916.

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In this study, the Gross–Pitaevskii equation perturbed with multiplicative time noise is under consideration numerically and analytically. The NLSE is a universal governing model that helps in evolution of complex fields that are used in dispersive media. For the numerical solution, we used the stochastic forward Euler (SFE) scheme. To find the exact solutions, we chose the techniques namely [Formula: see text]-model expansion. For the analysis of the proposed scheme, we checked the stability of the scheme with the help of Von-Neumann criteria and the consistency of the scheme with the mean of

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Baber, Muhammad Z., Aly R. Seadway, Nauman Ahmed, Muhammad S. Iqbal, and Muhammad W. Yasin. "Selection of solitons coinciding the numerical solutions for uniquely solvable physical problems: A comparative study for the nonlinear stochastic Gross–Pitaevskii equation in dispersive media." International Journal of Modern Physics B, December 21, 2022. http://dx.doi.org/10.1142/s0217979223501919.

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In this study, the Gross–Pitaevskii equation perturbed with multiplicative time noise is under consideration numerically and analytically. The NLSE is a universal governing model that helps in evolution of complex fields that are used in dispersive media. For the numerical solution, we used the stochastic forward Euler (SFE) scheme. To find the exact solutions, we chose the techniques namely [Formula: see text]-model expansion. For the analysis of the proposed scheme, we checked the stability of the scheme with the help of Von-Neumann criteria and the consistency of the scheme with the mean of

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