×

New algorithm for a class of nonlinear integro-differential equations in the reproducing kernel space. (English) Zbl 1094.65136

This paper is concerned with a new algorithm for giving the approximate solution of a class of nonlinear integro-differential equations in the reproducing kernel space. Two integro-differential equations are solved by the algorithm finding the separable solution. Numerical examples prove the adequacy of the numerical method.

MSC:

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Li, S.; Xu, D.; Zhao, H., Stability region of nonlinear integrodifferential equations, Applied Mathematics Letters, 13, 77-82 (2000) · Zbl 0974.45006
[2] Liu, L.; Wu, C.; Guo, F., Existence theorems of global solutions of initial value problems for nonlinear integrodifferential equations of mixed type in banach spaces and applications, Computers and Mathematics with Applications, 47, 13-22 (2004) · Zbl 1050.45003
[3] Pachpatle, D. G., On certain boundary value problems for nonlinear integrodifferential equations, Acta Mathematica Scientia, 412, 226-234 (1994) · Zbl 0812.45003
[4] Wang, Y. M., Asymptotic behavior of the numerical solutions for a system of nonlinear integrodifferential reaction-diffusion equations, Applied Numerical Mathematics, 39, 205-223 (2001) · Zbl 0994.65150
[5] Cui, M. G.; Zhongxing, D., On the best operator of interpolation, Math Numerical Sinica, 8, 2, 209-216 (1986) · Zbl 0605.41004
[6] Songlong, W.; Cui, M. G., Best approximate interpolation operator in space W, Journal of Computational Mathematics and Application, 3 (1997)
[7] Aronszajn, N., Theory of reproducing Kernel, Trans AMS, 68, 1-50 (1950) · Zbl 0037.20701
[8] Cui, M. G., Numerical Analysis in Reproducing Kelnel Space (2004), Science Publishers: Science Publishers Bejing, p. 15-27
[9] M.G. Cui, Lihong Yang, The exact solution of a kind of nonlinear operator equations, Applied Mathematics and Computation, to appear.; M.G. Cui, Lihong Yang, The exact solution of a kind of nonlinear operator equations, Applied Mathematics and Computation, to appear. · Zbl 1094.65136
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.