New Methods for Numerical Solution of One Class of Strongly Nonlinear Partial Differential Equations with Applications.

1987 ◽  
Author(s):  
V. I. Oliker ◽  
P. Waltman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
Strongly Nonlinear ◽  
New Methods

scholarly journals Numerical Solution of a Class of Nonlinear Partial Differential Equations by Using Barycentric Interpolation Collocation Method

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Hongchun Wu ◽  
Yulan Wang ◽  
Wei Zhang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Present Method ◽  
Nonlinear Partial Differential Equations ◽  
Economic Systems ◽  
Partial Differential ◽  
Barycentric Interpolation ◽  
Chemical Cycling

Partial differential equations (PDEs) are widely used in mechanics, control processes, ecological and economic systems, chemical cycling systems, and epidemiology. Although there are some numerical methods for solving PDEs, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, we give the meshless barycentric interpolation collocation method (MBICM) for solving a class of PDEs. Four numerical experiments are carried out and compared with other methods; the accuracy of the numerical solution obtained by the present method is obviously improved.

scholarly journals Numerical Solution of Coupled System of Nonlinear Partial Differential Equations Using Laplace-Adomian Decomposition Method

2016 ◽  
Vol 12 (8) ◽  
pp. 6530-6544
Author(s):  
Mohamed S M. Bahgat
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
Partial Differential ◽  
Adomian Decomposition

Aim of the paper is to investigate applications of Laplace Adomian Decomposition Method (LADM) on nonlinear physical problems. Some coupled system of non-linear partial differential equations (NLPDEs) are considered and solved numerically using LADM. The results obtained by LADM are compared with those obtained by standard and modified Adomian Decomposition Methods. The behavior of the numerical solution is shown through graphs. It is observed that LADM is an effective method with high accuracy with less number of components.

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