×

zbMATH — the first resource for mathematics

A new algorithm for calculating Adomian polynomials for nonlinear operators. (English) Zbl 1023.65108
Summary: A reliable technique for calculating Adomian polynomials for nonlinear operators will be developed. The new algorithm offers a promising approach for calculating Adomian polynomials for all forms of nonlinearity. The algorithm will be illustrated by studying suitable forms of nonlinearity. A nonlinear evolution model will be investigated.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35K90 Abstract parabolic equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] E.L. Allgower, On a discretization of y″+λyk=0, in: J.J.H. Miller (Ed.), Topics in Numerical Analysis, vol. II, Academic Press, New York, 1975. · Zbl 0365.65055
[2] Allgower, E.L.; McCormick, S.F., Newton’s method with mesh refinements for numerical solution of nonlinear two-point boundary value problems, Numer. math., 29, 237-260, (1978) · Zbl 0352.65048
[3] S. Busenberg, W. Huang, Stability and Hopf bifurcation for a population delay model with diffusion effects, J. Differential Equations 124 (1996) 81-107 · Zbl 0854.35120
[4] Cash, J.R., On the numerical integration of nonlinear two-point boundary value problems using iterated deferred corrections, part 1: A survey and comparison of some one-step formulae, Comput. math. appl., 12A, 1029-1048, (1986) · Zbl 0618.65071
[5] Cash, J.R., On the numerical integration of nonlinear two-point boundary value problems using iterated deferred corrections, part 2: the development and analysis of highly stable deferred correction formulae, SIAM J. numer. anal., 25, 862-882, (1988) · Zbl 0658.65070
[6] Cash, J.R.; Wright, M.H., Implementation issues in solving nonlinear equation for two-point boundary value problems, Computing, 45, 17-37, (1990) · Zbl 0721.65043
[7] Cash, J.R.; Wright, M.H., A deferred correction method for nonlinear two-point boundary value problems: implementation and numerical evaluation, SIAM J. sci. statist. comput., 12, 971-989, (1991) · Zbl 0727.65070
[8] J.R. Cash, M.H. Wright, The code twpbvp.f under the directory of netlib, available in http://www.netlib.no/netlib/ode/, 1995
[9] P.J. Davis, P. Rabinowitz, Methods of Numerical Integration, Academic Press, Florida, 1984 · Zbl 0537.65020
[10] Descloux, J.; Rappaz, J., A nonlinear inverse power method with shift, SIAM J. numer. anal., 20, 1147-1152, (1983) · Zbl 0536.65046
[11] Duvallet, J., Computation of solutions of two-point boundary value problems by a simplical homotopy algorithm, Lectures in appl. math., 26, 135-150, (1990)
[12] Georg, K., On the convergence of an inverse iteration method for nonlinear elliptic eigenvalue problems, Numer. math., 32, 69-74, (1979) · Zbl 0431.65065
[13] Jacobs, S.J., A pseudo spectral method for two-point boundary value problems, J. comput. phys., 88, 169-182, (1990) · Zbl 0703.65040
[14] Jankowski, T., On the convergence of multistep methods for nonlinear two-point boundary value problems, Ann. polon. math., 53, 185-200, (1991) · Zbl 0746.65060
[15] Kalaba, R.E.; Spingarn, K., Numerical solution of a nonlinear two-point boundary value problem by an imbedding method, Nonlinear anal. TMA, 1, 129-133, (1977) · Zbl 0358.65068
[16] Ji Cheng Jin, Numerical solutions to nonlinear two-point boundary value problems with multiple solutions, Natur. Sci. J. Xiangtan Univ. 14 (1992) 1-7 (in Chinese)
[17] J.W.-H. So, Y. Yang, Dirichlet problem for the diffusive Nicholson’s blowflies equation, J. Differential Equations, 150 (1998) 317-348 · Zbl 0923.35195
[18] Watson, L.T.; Scott, L.R., Solving Galerkin approximations to nonlinear two-point boundary value problems by a globally convergent homotopy method, SIAM J. sci. statist. comput., 8, 768-789, (1987) · Zbl 0645.65043
[19] J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer, New York, 1996 · Zbl 0870.35116
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.