Abstract
This paper proposes an effective improvement of the homotopy perturbation method (HPM) by using Jacobi and He's polynomials to solve some nonlinear ordinary differential equations. With this method, the source terms of ordinary differential equations can be expanded in series of shifted Jacobi polynomials. Numerical results are given in this paper to illustrate the reliability of this method with nonlinear ordinary differential equations. Key words: Homotopy perturbation method (HPM), shifted Jacobi polynomials, nonlinear ordinary differential equations.
Highlights
In recent years, the subject of differential calculus received attention in regards to effective numerical methods for solving linear and nonlinear differential equations
This paper proposes an effective improvement of the homotopy perturbation method (HPM) by using Jacobi and He's polynomials to solve some nonlinear ordinary differential equations
The source terms of ordinary differential equations can be expanded in series of shifted Jacobi polynomials
Summary
This paper proposes an effective improvement of the homotopy perturbation method (HPM) by using Jacobi and He's polynomials to solve some nonlinear ordinary differential equations. With this method, the source terms of ordinary differential equations can be expanded in series of shifted Jacobi polynomials. Numerical results are given in this paper to illustrate the reliability of this method with nonlinear ordinary differential equations
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