Feyed Ben Zitoun and Yves Cherruault
The purpose of this paper is to present a method for solving nonlinear differential equations with constant and/or variable coefficients and with initial and/or boundary…
Abstract
Purpose
The purpose of this paper is to present a method for solving nonlinear differential equations with constant and/or variable coefficients and with initial and/or boundary conditions.
Design/methodology/approach
The method converts the nonlinear boundary value problem into a system of nonlinear algebraic equations. By solving this system, the solution is determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use, and highly accurate.
Findings
The proposed technique allows us to obtain an approximate solution in a series form. Test problems are given to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well suited for solving nonlinear differential equations.
Originality/value
The present approach provides a reliable technique, which avoids the tedious work needed by classical techniques and existing numerical methods. The nonlinear problem is solved without linearizing or discretizing the nonlinear terms of the equation. The method does not require physically unrealistic assumptions, linearization, discretization, perturbation, or any transformation in order to find the solutions of the given problems.
Details
Keywords
Feyed Ben Zitoun and Yves Cherruault
The purpose of this paper is to present a method for solving nonlinear integro‐differential equations with constant/variable coefficients and with initial/boundary conditions.
Abstract
Purpose
The purpose of this paper is to present a method for solving nonlinear integro‐differential equations with constant/variable coefficients and with initial/boundary conditions.
Design/methodology/approach
The method converts the given problem into a system of nonlinear algebraic equations. By solving this system, the solution is determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use and highly accurate.
Findings
The proposed technique allows an approximate solution in a series form to be obtained. Test problems are solved to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well suited for solving nonlinear integro‐differential equations.
Originality/value
The present approach provides a reliable technique which avoids the tedious work needed by the classical techniques.
Details
Keywords
Feyed Ben Zitoun and Yves Cherruault
The purpose of this paper is to present a method for solving nonlinear integral equations of the second and third kind.
Abstract
Purpose
The purpose of this paper is to present a method for solving nonlinear integral equations of the second and third kind.
Design/methodology/approach
The method converts the nonlinear integral equation into a system of nonlinear equations. By solving the system, the solution can be determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use, and highly accurate.
Findings
The proposed technique allows the authors to obtain an approximate solution in a series form. Test problems are given to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well‐suited for solving nonlinear integral equations.
Originality/value
The present approach provides a reliable technique that avoids the difficulties and massive computational work if compared with the traditional techniques and does not require discretization in order to find solutions to the given problems.
Details
Keywords
Feyed Ben Zitoun and Yves Cherruault
The purpose of this paper is to present a new algorithm for solving nonlinear boundary value problems (BVPs).
Abstract
Purpose
The purpose of this paper is to present a new algorithm for solving nonlinear boundary value problems (BVPs).
Design/methodology/approach
The method converts the nonlinear BVP into a system of nonlinear equations. By solving the system, the solution can be determined. Comparing the methodology with some known techniques shows that the present approach is simple, easy to use and highly accurate.
Findings
The proposed technique allows us to obtain an approximate solution in a series form which satisfies all the given conditions. Test problems are given to illustrate the pertinent features of the method. The accuracy of the numerical results indicates that the technique is efficient and well suited for solving nonlinear differential equations with initial and boundary conditions.
Originality/value
The paper provides a reliable technique which avoids the tedious work needed by classical techniques and existing numerical methods and does not require discretization in order to find the solutions of the given problems.