2017
DOI: 10.1002/num.22223
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On solutions to the second‐order partial differential equations by two accurate methods

Abstract: In this article, we investigate the reproducing kernel method and the difference schemes method for solving the secondorder partial differential equations. Numerical results have been shown to prove the efficiency of the methods. Results prove that the methods are very effective. K E Y W O R D Sdifference schemes method, partial differential equations, reproducing kernel Hilbert space Numer Methods Partial Differential Eq. 2017;1-15.wileyonlinelibrary.com/journal/num

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Cited by 13 publications
(11 citation statements)
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“…In [16], Liu has studied fractional difference approximations for time-fractional telegraph equation. Modanli and Akgül [12] have worked the second-order partial differential equations by two accurate methods. Finally, Modanli and Akgul [13] have solved the fractional telegraph differential equations by theta-method.…”
Section: Introductionmentioning
confidence: 99%
“…In [16], Liu has studied fractional difference approximations for time-fractional telegraph equation. Modanli and Akgül [12] have worked the second-order partial differential equations by two accurate methods. Finally, Modanli and Akgul [13] have solved the fractional telegraph differential equations by theta-method.…”
Section: Introductionmentioning
confidence: 99%
“…To achieve this goal, we must first construct reproducing kernel spaces and their kernels such that satisfy the nonlocal conditions, and then implement RKM without Gram–Schmidt orthogonalization process on the problem (1). Some numerical methods such as RKM with Gram–Schmidt orthogonalization process (see [19–22]) have already been used by researchers for parabolic partial differential equation (PPDE) with nonlocal conditions [23–26] and indeed here we improve the approximate solutions to the problem (1) with more accuracy. Additionally, we prove the stability theorem of the method and provide error analysis for this technique.…”
Section: Introductionmentioning
confidence: 99%
“…Recently, the RKM has been improved and successfully applied in obtaining approximations of solutions for many initial and boundary problems that appear in natural sciences and engineering. The RKM was successfully used for solving the Thomas-Fermi equation [28], the Poisson-Boltzmann equation for semiconductor devices [29], variable-order fractional differential equations [30] and second-order partial differential equations [31] and others [32][33][34]. Moreover, Cui and Lin [24] have efficiently solved obstacle third-order BVP using RKM.…”
Section: Introductionmentioning
confidence: 99%