Chebyshev Collocation Method for Solving Linear Differential Equations

Discrete Collocation Method for Solving Fredholm Volterra Intergro-Differential Equations

Rational Chebyshev Collocation Method for Solving Nonlinear Ordinary Differential Equations of Lane-emden Type

Lane-Emden equation is a nonlinear singular equation that plays an important role in the astrophysics. In this paper, we have applied the collocation method based on rational Chebyshev functions to solve Lane-Emden type equations. The method reduces solving the nonlinear ordinary differential equation to solving a system of nonlinear algebraic equations. The comparison of the results with the o...

A Chebyshev functions method for solving linear and nonlinear fractional differential equations based on Hilfer fractional derivative

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...

The Petrov-Galerkin Method and Chebyshev Multiwavelet Basis for Solving Integro-Differential Equations

 Abstract: There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For ...

Discrete Collocation Method for Solving Fredholm–Volterra Integro–Differential Equations

In this article we use discrete collocation method for solving Fredholm–Volterra integro– differential equations, because these kinds of integral equations are used in applied sciences and engineering such as models of epidemic diffusion, population dynamics, reaction–diffusion in small cells. Also the above integral equations with convolution kernel will be solved by discrete collocation metho...