Improvement of the homotopy perturbation method to nonlinear problems
J. F. Alzaidi,A. A. Alderremy +1 more
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TLDR
In this article, the homotopy perturbation method was improved by using Jacobi and He's polynomials to solve some nonlinear ordinary differential equations, where the source terms of ODEs can be expanded in series of shifted Jacobi polynomial.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.read more
Citations
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Application of homotopy perturbation method to an sir mumps model
TL;DR: In this article, the spread of mumps in a closed population is investigated using a SIR compartmental model and the method of homotopy perturbation is adopted to derive the theoretical solutions of the system.
Journal ArticleDOI
A study of obstacle problems using homotopy perturbation method
TL;DR: In this paper, the homotopy perturbation method (HPM) is used to solve multiple-point boundary value problems arising in obstacle, unilateral and contact problems, where convergent approximate solutions are constructed such that the exact boundary conditions are satisfied.
References
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Journal ArticleDOI
Homotopy perturbation technique
TL;DR: In this paper, the homotopy perturbation technique does not depend upon a small parameter in the equation and can be obtained uniformly valid not only for small parameters, but also for very large parameters.
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Addendum:. New Interpretation of Homotopy Perturbation Method
TL;DR: In this article, a guided tour through the mathematics needed for a proper understanding of homotopy perturbation method as applied to various nonlinear problems is presented, and a new interpretation of the concept of constant expansion is given.
Journal ArticleDOI
Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method
TL;DR: A new method for solving fuzzy differential equations based on the reproducing kernel theory under strongly generalized differentiability is presented, showing potentiality, generality, and superiority of the method as compared with other well-known methods.
Journal ArticleDOI
Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method
TL;DR: In this article, homotopy perturbation method (HPM) is applied to solve fractional partial differential equations (PDEs) with proportional delay in t and shrinking in x.
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An efficient method for quadratic Riccati differential equation
TL;DR: In this paper, a new form of homotopy perturbation method (NHPM) has been adopted for solving the quadratic Riccati differential equation, where the solution is considered as a Taylor series expansion converges rapidly to the exact solution of the nonlinear equation.