6 research outputs found
An approximation method for the solution of nonlinear integral equations
A Chebyshev collocation method has been presented to solve nonlinear integral equations in terms of Chebyshev polynomials. This method transforms the integral equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Chebyshev coefficients. Finally, some examples are presented to illustrate the method and results discussed. (c) 2005 Elsevier Inc. All rights reserved
A new exponential Jacobi pseudospectral method for solving high-order ordinary differential equations
Approximate solution of linear and nonlinear fractional differential equations under m-point local and nonlocal boundary conditions
Fredholm integro-differential-difference equations
In this study, a matrix method is developed to solve approximately the most general higher order linear Fredholm integro-differential-difference equations with variable coefficients under the mixed conditions in terms of Taylor polynomials. This technique reduces the problem into the linear algebraic system. The method is valid for any combination of differential, difference and integral equations. An initial value problem and a boundary value problem are also presented to illustrate the accuracy and efficiency of the method. Copyright (c) 2012 John Wiley & Sons, Ltd
Bernstein collocation method for solving nonlinear differential equations
In this study, a collocation method based on Bernstein polynomials is developed for solution of the nonlinear ordinary differential equations with variable coefficients, under the mixed conditions. These equations are expressed as linear ordinary differential equations via quasilinearization method iteratively. By using the Bernstein collocation method, solutions of these linear equations are approximated. Combining the quasilinearization and the Bernstein collocation methods, the approximation solution of nonlinear differential equations is obtained. Moreover, some numerical solutions are given to illustrate the accuracy and implementation of the method
Chebyshev Series
By the use of the Chebyshev series, a direct computational method for solving the higher order nonlinear differential equations has been developed in this paper. This method transforms the nonlinear differential equation into the matrix equation, which corresponds to a system of nonlinear algebraic equations with unknown Chebyshev coefficients, via Chebyshev collocation points. The solution of this system yields the Chebyshev coefficients of the solution function. An algorithm for this nonlinear system is also proposed in this paper. The method is valid for both initial-value and boundary-value problems. Several examples are presented to illustrate the accuracy and effectiveness of the method. (C) 2010 Elsevier Inc. All rights reserved