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Journal articles on the topic 'Conjugate boundary value problems'

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Published: 14 March 2023

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1

Agarwal, R. P., and D. O'Regan. "Discrete conjugate boundary value problems." Applied Mathematics Letters 13, no. 2 (February 2000): 97–104. http://dx.doi.org/10.1016/s0893-9659(99)00171-8.

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2

Li, Weifeng, and Jinyuan Du. "Linear conjugate boundary value problems." Wuhan University Journal of Natural Sciences 12, no. 6 (November 2007): 985–91. http://dx.doi.org/10.1007/s11859-007-0037-5.

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3

Chuan-Rong, Wang, and Yang Qiao-Lin. "Linear conjugate boundary value problems." Complex Variables, Theory and Application: An International Journal 31, no. 2 (October 1996): 105–19. http://dx.doi.org/10.1080/17476939608814952.

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4

Palamides, P. K. "Conjugate boundary value problems, via Sperner's lemma." Nonlinear Analysis: Theory, Methods & Applications 46, no. 2 (October 2001): 299–308. http://dx.doi.org/10.1016/s0362-546x(00)00124-3.

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5

Wong, P. J. Y. "Triple positive solutions of conjugate boundary value problems." Computers & Mathematics with Applications 36, no. 9 (November 1998): 19–35. http://dx.doi.org/10.1016/s0898-1221(98)00190-4.

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6

Agarwal, Ravi P., Martin Bohner, and Patricia J. Y. Wong. "Positive solutions and eigenvalues of conjugate boundary value problems." Proceedings of the Edinburgh Mathematical Society 42, no. 2 (June 1999): 349–74. http://dx.doi.org/10.1017/s0013091500020307.

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We consider the following boundary value problemwhere λ > 0 and 1 ≤ p ≤ n – 1 is fixed. The values of λ are characterized so that the boundary value problem has a positive solution. Further, for the case λ = 1 we offer criteria for the existence of two positive solutions of the boundary value problem. Upper and lower bounds for these positive solutions are also established for special cases. Several examples are included to dwell upon the importance of the results obtained.
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7

Yao, Qingliu. "Positive solution to a singular $(k,n-k)$ conjugate boundary value problem." Mathematica Bohemica 136, no. 1 (2011): 69–79. http://dx.doi.org/10.21136/mb.2011.141451.

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8

Wong, Patricia J. Y., and Ravi P. Agarwal. "Multiple Solutions of Generalized Multipoint Conjugate Boundary Value Problems." gmj 6, no. 6 (December 1999): 567–90. http://dx.doi.org/10.1515/gmj.1999.567.

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Abstract We consider the boundary value problem 𝑦(𝑛) (𝑡) = 𝑃(𝑡, 𝑦), 𝑡 ∈ (0, 1) 𝑦(𝑗) (𝑡𝑖) = 0, 𝑗 = 0, . . . , 𝑛𝑖 – 1, 𝑖 = 1, . . . , 𝑟, where 𝑟 ≥ 2, 𝑛𝑖 ≥ 1 for 𝑖 = 1, . . . , 𝑟, and 0 = 𝑡1 < 𝑡2 < ⋯ < 𝑡𝑟 = 1. Criteria are offered for the existence of double and triple ‘positive’ (in some sense) solutions of the boundary value problem. Further investigation on the upper and lower bounds for the norms of these solutions is carried out for special cases. We also include several examples to illustrate the importance of the results obtained.
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9

Davis, John M., Paul W. Eloe, and Johnny Henderson. "Triple Positive Solutions for Multipoint Conjugate Boundary Value Problems." gmj 6, no. 5 (October 1999): 415–20. http://dx.doi.org/10.1515/gmj.1999.415.

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Abstract For the 𝑛th order nonlinear differential equation 𝑦(𝑛)(𝑡) = 𝑓(𝑦(𝑡)), 𝑡 ∈ [0, 1], satisfying the multipoint conjugate boundary conditions, 𝑦(𝑗)(𝑎𝑖) = 0, 1 ≤ 𝑖 ≤ 𝑘, 0 ≤ 𝑗 ≤ 𝑛𝑖 – 1, 0 = 𝑎1 < 𝑎2 < ⋯ < 𝑎𝑘 = 1, and , where 𝑓 : ℝ → [0, ∞) is continuous, growth condtions are imposed on 𝑓 which yield the existence of at least three solutions that belong to a cone.
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10

Kaufmann, Eric R., and Nickolai Kosmatov†. "Singular Conjugate Boundary Value Problems on a Time Scale." Journal of Difference Equations and Applications 10, no. 2 (February 2004): 119–27. http://dx.doi.org/10.1080/1023619031000114332.

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11

Wong, Patricia J. Y., and Ravi P. Agarwal. "Eigenvalue theorems for discrete multipoint conjugate boundary value problems." Journal of Computational and Applied Mathematics 113, no. 1-2 (January 2000): 227–40. http://dx.doi.org/10.1016/s0377-0427(99)00258-7.

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12

Wong, P. J. Y. "Triple positive solutions of conjugate boundary value problems II." Computers & Mathematics with Applications 40, no. 4-5 (August 2000): 537–57. http://dx.doi.org/10.1016/s0898-1221(00)00178-4.

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13

Webb, J. R. L. "Nonlocal conjugate type boundary value problems of higher order." Nonlinear Analysis: Theory, Methods & Applications 71, no. 5-6 (September 2009): 1933–40. http://dx.doi.org/10.1016/j.na.2009.01.033.

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14

Agarwal, R. P., M. Bohner, and P. J. Y. Wong. "Eigenvalues and eigenfunctions of discrete conjugate boundary value problems." Computers & Mathematics with Applications 38, no. 3-4 (August 1999): 159–83. http://dx.doi.org/10.1016/s0898-1221(99)00192-3.

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15

Eloe, Paul W., and Johnny Henderson. "Singular Nonlinear (k, n−k) Conjugate Boundary Value Problems." Journal of Differential Equations 133, no. 1 (January 1997): 136–51. http://dx.doi.org/10.1006/jdeq.1996.3207.

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16

Qiu, Yu-Yang. "Numerical method to a class of boundary value problems." Thermal Science 22, no. 4 (2018): 1877–83. http://dx.doi.org/10.2298/tsci1804877q.

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A class of boundary value problems can be transformed uniformly to a least square problem with Toeplitz constraint. Conjugate gradient least square, a matrix iteration method, is adopted to solve this problem, and the solution process is elucidated step by step so that the example can be used as a paradigm for other applications.
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17

Lan, K. Q. "Multiple positive solutions of conjugate boundary value problems with singularities." Applied Mathematics and Computation 147, no. 2 (January 2004): 461–74. http://dx.doi.org/10.1016/s0096-3003(02)00739-7.

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18

Jiang, Weihua, and Jinlian Zhang. "Positive solutions for conjugate boundary value problems in Banach spaces." Nonlinear Analysis: Theory, Methods & Applications 71, no. 3-4 (August 2009): 723–29. http://dx.doi.org/10.1016/j.na.2008.10.104.

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19

Eloe, Paul W., Darrel Hankerson, and Johnny Henderson. "Positive solutions and conjugate points for multipoint boundary value problems." Journal of Differential Equations 95, no. 1 (January 1992): 20–32. http://dx.doi.org/10.1016/0022-0396(92)90041-k.

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20

Lou, Bendong. "Solutions for superlinear ( n − 1, 1) conjugate boundary value problems." Acta Mathematica Scientia 21, no. 2 (April 2001): 259–64. http://dx.doi.org/10.1016/s0252-9602(17)30408-3.

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21

Nicolaides, R. A. "Deflation of Conjugate Gradients with Applications to Boundary Value Problems." SIAM Journal on Numerical Analysis 24, no. 2 (April 1987): 355–65. http://dx.doi.org/10.1137/0724027.

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22

Tikhomirov, V. V. "Optimal control of some non-self-conjugate boundary-value problems." Computational Mathematics and Modeling 9, no. 1 (January 1998): 94–101. http://dx.doi.org/10.1007/bf02404089.

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23

Eloe, Paul W., and Johnny Henderson. "Positive solutions for (n − 1, 1) conjugate boundary value problems." Nonlinear Analysis: Theory, Methods & Applications 28, no. 10 (May 1997): 1669–80. http://dx.doi.org/10.1016/0362-546x(95)00238-q.

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24

Agarwal, Ravi P., and Donal O'Regan. "Positive Solutions for (p,n−p) Conjugate Boundary Value Problems." Journal of Differential Equations 150, no. 2 (December 1998): 462–73. http://dx.doi.org/10.1006/jdeq.1998.3501.

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25

Gustafson, Grant B. "Uniqueness intervals and two–point boundary value problems." Tatra Mountains Mathematical Publications 43, no. 1 (December 1, 2009): 91–97. http://dx.doi.org/10.2478/v10127-009-0028-3.

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Abstract Consider a linear nth order differential equation with continuous coefficients and continuous forcing term. The maximal uniqueness interval for a classical 2-point boundary value problem will be calculated by an algorithm that uses an auxiliary linear system of differential equations, called a Mikusinski system. This system always has higher order than n. The algorithm leads to a graphical representation of the uniqueness profile and to a new method for solving 2-point boundary value problems. The ideas are applied to construct a graphic for the conjugate function associated with the nth order linear homogeneous differential equation. Details are given about how to solve classical 2-point boundary value problems, using auxiliary Mikusinski systems and Green’s function.
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26

Chyan, Chuan Jen, and Patricia J. Y. Wong. "MULTIPLE POSITIVE SOLUTIONS OF CONJUGATE BOUNDARY VALUE PROBLEMS ON TIME SCALES." Taiwanese Journal of Mathematics 11, no. 2 (June 2007): 421–45. http://dx.doi.org/10.11650/twjm/1500404700.

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27

Cui, Yujun, and Yumei Zou. "Monotone iterative technique for $(k, n-k)$ conjugate boundary value problems." Electronic Journal of Qualitative Theory of Differential Equations, no. 69 (2015): 1–11. http://dx.doi.org/10.14232/ejqtde.2015.1.69.

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28

Zu, Li, Daqing Jiang, Yongjie Gai, Donal O’Regan, and Haiyin Gao. "Weak singularities and existence of solutions to conjugate boundary value problems." Nonlinear Analysis: Real World Applications 10, no. 5 (October 2009): 2627–32. http://dx.doi.org/10.1016/j.nonrwa.2008.05.013.

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29

Zheng, Bo. "Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value Problems." Discrete Dynamics in Nature and Society 2010 (2010): 1–26. http://dx.doi.org/10.1155/2010/364079.

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We consider the existence and multiplicity of solutions to discrete conjugate boundary value problems. A generalized asymptotically linear condition on the nonlinearity is proposed, which includes the asymptotically linear as a special case. By classifying the linear systems, we define index functions and obtain some properties and the concrete computation formulae of index functions. Then, some new conditions on the existence and multiplicity of solutions are obtained by combining some nonlinear analysis methods, such as Leray-Schauder principle and Morse theory. Our results are new even for the case of asymptotically linear.
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30

Ma, Ruyun. "Positive Solutions for Semipositone (k,n−k) Conjugate Boundary Value Problems." Journal of Mathematical Analysis and Applications 252, no. 1 (December 2000): 220–29. http://dx.doi.org/10.1006/jmaa.2000.6987.

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31

Sun, Qiao, and Yujun Cui. "Solvability of (k,n-k) Conjugate Boundary Value Problems with Integral Boundary Conditions at Resonance." Journal of Function Spaces 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/3454879.

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We investigate a (k,n-k) conjugate boundary value problem with integral boundary conditions. By using Mawhin continuation theorem, we study the solvability of this boundary value problem at resonance. It is shown that the boundary value problem (-1)n-kφ(n)(x)=fx,φx,φ′x,…,φ(n-1)(x), x∈[0,1], φ(i)(0)=φ(j)(1)=0, 1≤i≤k-1, 0≤j≤n-k-1, φ(0)=∫01φ(x)dA(x) has at least one solution under some suitable conditions.
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32

JIANG, Daqing, and Huizhao LIU. "EXISTENCE OF POSITIVE SOLUTIONS TO (k, n-k) CONJUGATE BOUNDARY VALUE PROBLEMS †." Kyushu Journal of Mathematics 53, no. 1 (1999): 115–25. http://dx.doi.org/10.2206/kyushujm.53.115.

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33

Henderson, Johnny, and William Yin. "Singular (k, n − k) boundary value problems between conjugate and right focal." Journal of Computational and Applied Mathematics 88, no. 1 (February 1998): 57–69. http://dx.doi.org/10.1016/s0377-0427(97)00207-0.

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34

Eloe, P. W., and P. L. Saintignon. "Method of Forced Monotonicity for Conjugate type Boundary Value Problems for Ordinary Differential Equations." Canadian Mathematical Bulletin 31, no. 1 (March 1, 1988): 79–84. http://dx.doi.org/10.4153/cmb-1988-012-0.

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AbstractLet I = [a, b] ⊆ R and let L be an nth order linear differential operator defined on Cn(I). Let 2 ≦ k ≦ n and let a ≦ x1 < x2 < … < xn = b. A method of forced mono tonicity is used to construct monotone sequences that converge to solutions of the conjugate type boundary value problem (BVP) Ly = f(x, y),y(i-1) = rij where 1 ≦i ≦ mj, 1 ≦ j ≦ k, mj = n, and f : I X R → R is continuous. A comparison theorem is employed and the method requires that the Green's function of an associated BVP satisfies certain sign conditions.
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35

Zhao, Yulin. "Positive Solutions for (k,n−k) Conjugate Multipoint Boundary Value Problems in Banach Spaces." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/727468.

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By means of the fixed point index theory of strict-set contraction operator, we study the existence of positive solutions for the multipoint singular boundary value problem(-1)n-kun(t)=f(t,ut),0<t<1,n≥2,1≤k≤n-1,u(0)=∑i=1m-2‍aiu(ξi),u(i)(0)=u(j)(1)=θ,1≤i≤k−1,0≤j≤n−k−1in a real Banach spaceE, whereθis the zero element ofE,0<ξ1<ξ2<⋯<ξm-2<1,ai∈[0,+∞),i=1,2,…,m-2.As an application, we give two examples to demonstrate our results.
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36

Lin, Xiaoning, Daqing Jiang, and Xiaoyue Li. "Existence and uniqueness of solutions for singular (k, n - k) conjugate boundary value problems." Computers & Mathematics with Applications 52, no. 3-4 (August 2006): 375–82. http://dx.doi.org/10.1016/j.camwa.2006.03.019.

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37

Glowinski, R., H. B. Keller, and L. Reinhart. "Continuation-Conjugate Gradient Methods for the Least Squares Solution of Nonlinear Boundary Value Problems." SIAM Journal on Scientific and Statistical Computing 6, no. 4 (October 1985): 793–832. http://dx.doi.org/10.1137/0906055.

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38

Kong, Lingbin, and Junyu Wang. "The Green's Function for (k,n−k) Conjugate Boundary Value Problems and Its Applications." Journal of Mathematical Analysis and Applications 255, no. 2 (March 2001): 404–22. http://dx.doi.org/10.1006/jmaa.2000.7158.

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39

Мартыненко, С. И. "On the approximation error in the problems of conjugate convective heat transfer." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 4 (September 10, 2019): 438–43. http://dx.doi.org/10.26089/nummet.v20r438.

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Рассмотрено влияние малых возмущений границы области на погрешность аппроксимации модельной краевой задачи. Показано, что игнорирование малых возмущений границы приводит к дополнительной погрешности аппроксимации исходной дифференциальной задачи, не связанной с шагом сетки. Полученные результаты представляют интерес для математического моделирования сопряженного теплообмена, моделирования течений с поверхностными химическими реакциями и других приложений, связанных с течениями рабочих сред вблизи шероховатых поверхностей. The effects of small boundary perturbation on the approximation error for a model boundary value problem are considered. It is shown that the ignorance of small perturbations of the boundary leads to an additional approximation error in the original differential problem. This error is independent of mesh size. The obtained results are of interest for the mathematical modeling of conjugate heat transfer, the modeling of flows with surface chemical reactions and other applications related to fluid flows near rough surfaces.
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40

Wang, Yongqing. "Existence of Uniqueness and Nonexistence Results of Positive Solution for Fractional Differential Equations Integral Boundary Value Problems." Journal of Function Spaces 2018 (December 4, 2018): 1–7. http://dx.doi.org/10.1155/2018/1547293.

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In this paper, we consider a class of fractional differential equations with conjugate type integral conditions. Both the existence of uniqueness and nonexistence of positive solution are obtained by means of the iterative technique. The interesting point lies in that the assumption on nonlinearity is closely associated with the spectral radius corresponding to the relevant linear operator.
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41

FAN, Jinjun, and Yinghua YANG. "Singular (n-1,n) Conjugate Boundary Value Problems in Banach Spaces." Acta Analysis Functionalis Applicata 12, no. 1 (May 24, 2010): 79–82. http://dx.doi.org/10.3724/sp.j.1160.2010.00079.

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42

Marasanov, V. V., A. V. Sharko, and A. A. Sharko. "Boundary-Value Problems of Determining the Energy Spectrum of Acoustic Emission Signals in Conjugate Continuous Media." Cybernetics and Systems Analysis 55, no. 5 (September 2019): 851–59. http://dx.doi.org/10.1007/s10559-019-00195-8.

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43

Hao, Xinan, Peiguo Zhang, and Lishan Liu. "Iterative solutions of singular(k,n−k)conjugate boundary value problems with dependence on the derivatives." Applied Mathematics Letters 27 (January 2014): 64–69. http://dx.doi.org/10.1016/j.aml.2013.08.003.

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44

Zhang, Xingqiu, Zhuyan Shao, and Qiuyan Zhong. "Positive solutions for semipositone(k,n−k)conjugate boundary value problems with singularities on space variables." Applied Mathematics Letters 72 (October 2017): 50–57. http://dx.doi.org/10.1016/j.aml.2017.04.007.

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45

Chen, R. S., Edward K. N. Yung, C. H. Chan, and D. G. Fang. "Application of the preconditioned conjugate-gradient algorithm to the edge FEM for electromagnetic boundary-value problems." Microwave and Optical Technology Letters 27, no. 4 (2000): 235–38. http://dx.doi.org/10.1002/1098-2760(20001120)27:4<235::aid-mop5>3.0.co;2-8.

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46

Glowinski, Roland, and Qiaolin He. "A Least-Squares/Fictitious Domain Method for Linear Elliptic Problems with Robin Boundary Conditions." Communications in Computational Physics 9, no. 3 (March 2011): 587–606. http://dx.doi.org/10.4208/cicp.071009.160310s.

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AbstractIn this article, we discuss a least-squares/fictitious domain method for the solution of linear elliptic boundary value problems with Robin boundary conditions. Let Ω and ω be two bounded domains of Rd such that ω̅⊂Ω. For a linear elliptic problem in Ω\ω̅ with Robin boundary condition on the boundary ϒ of ω, our goal here is to develop a fictitious domain method where one solves a variant of the original problem on the full Ω, followed by a well-chosen correction over ω. This method is of the virtual control type and relies on a least-squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. Numerical results obtained when applying our method to the solution of two-dimensional elliptic and parabolic problems are given; they suggest optimal order of convergence.
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47

Tkachev, Alexander, Dmitry Chernoivan, and Nikolay Savelov. "A Combined Mesh-Free Method for Solving the Mixed Boundary Value Problems in Modeling the Potential Physical Fields." Известия высших учебных заведений. Электромеханика 65, no. 4 (2022): 3–14. http://dx.doi.org/10.17213/0136-3360-2022-4-3-14.

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The article describes a combined mesh-free method for solving mixed boundary value problems for the Laplace equa-tion arising from the analysis of potential physical fields in homogeneous media. The solution using mesh-free meth-ods of fundamental solutions and the Monte Carlo method is found. The modification of these methods is carried out taking into account the features that arise when setting mixed boundary conditions at the computational domain boundary. The conjugate fundamental solutions of the Laplace equation and the procedure of random walk by spheres are used, taking into account the features of constructing the trajectory of motion, close to the boundary part on which the normal derivative is set. The article proposes a procedure for the combined implementation of both two mesh-free methods of fundamental solutions and the Monte Carlo method which provides higher calculations accura-cy. The combined method was verified using benchmarks which are the results obtained using the reference solution squared and the solution obtained by the finite element method using the FEMM 4.2 software package when analyzing the electromagnet gap field in the vicinity of the.
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48

GRAVVANIS, GEORGE A., and KONSTANTINOS M. GIANNOUTAKIS. "ON THE RATE OF CONVERGENCE AND COMPLEXITY OF NORMALIZED IMPLICIT PRECONDITIONING FOR SOLVING FINITE DIFFERENCE EQUATIONS IN THREE SPACE VARIABLES." International Journal of Computational Methods 01, no. 02 (September 2004): 367–86. http://dx.doi.org/10.1142/s0219876204000174.

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Normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite difference method of partial differential equations in three space variables, are presented. Normalized implicit preconditioned conjugate gradient-type schemes in conjunction with normalized approximate factorization procedures are presented for the efficient solution of sparse linear systems. The convergence analysis with theoretical estimates on the rate of convergence and computational complexity of the normalized implicit preconditioned conjugate gradient method are also given. Application of the proposed method on characteristic three dimensional boundary value problems is discussed and numerical results are given.
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49

Iavernaro, Felice, and Francesca Mazzia. "A Fourth Order Symplectic and Conjugate-Symplectic Extension of the Midpoint and Trapezoidal Methods." Mathematics 9, no. 10 (May 13, 2021): 1103. http://dx.doi.org/10.3390/math9101103.

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The paper presents fourth order Runge–Kutta methods derived from symmetric Hermite–Obreshkov schemes by suitably approximating the involved higher derivatives. In particular, starting from the multi-derivative extension of the midpoint method we have obtained a new symmetric implicit Runge–Kutta method of order four, for the numerical solution of first-order differential equations. The new method is symplectic and is suitable for the solution of both initial and boundary value Hamiltonian problems. Moreover, starting from the conjugate class of multi-derivative trapezoidal schemes, we have derived a new method that is conjugate to the new symplectic method.
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50

Mukhigulashvili, Sulkhan. "Some two-point boundary value problems for systems of higher order functional differential equations." MATHEMATICA SCANDINAVICA 127, no. 2 (August 31, 2021): 382–404. http://dx.doi.org/10.7146/math.scand.a-126021.

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In the paper we study the question of the solvability and unique solvability of systems of the higher order differential equations with the argument deviations \begin{equation*} u_i^{(m_i)}(t)=p_i(t)u_{i+1}(\tau _{i}(t))+ q_i(t), (i=\overline {1, n}), \text {for $t\in I:=[a, b]$}, \end{equation*} and \begin{equation*}u_i^{(m_i)} (t)=F_{i}(u)(t)+q_{0i}(t), (i = \overline {1, n}), \text {for $ t\in I$}, \end{equation*} under the conjugate $u_i^{(j_1-1)}(a)=a_{i j_1}$, $u_i^{(j_2-1)}(b)=b_{i j_2}$, $j_1=\overline {1, k_i}$, $j_2=\overline {1, m_i-k_i}$, $i=\overline {1, n}$, and the right-focal $u_i^{(j_1-1)}(a)=a_{i j_1}$, $u_i^{(j_2-1)}(b)=b_{i j_2}$, $j_1=\overline {1, k_i}$, $j_2=\overline {k_i+1,m_i}$, $i=\overline {1, n}$, boundary conditions, where $u_{n+1}=u_1, $ $n\geq 2, $ $m_i\geq 2, $ $p_i \in L_{\infty }(I; R), $ $q_i, q_{0i}\in L(I; R), $ $\tau _i\colon I\to I$ are the measurable functions, $F_i$ are the local Caratheodory's class operators, and $k_i$ is the integer part of the number $m_i/2$.In the paper are obtained the efficient sufficient conditions that guarantee the unique solvability of the linear problems and take into the account explicitly the effect of argument deviations, and on the basis of these results are proved new conditions of the solvability and unique solvability for the nonlinear problems.
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