First order smooth composite Chebyshev finite difference method for solving coupled Lane-Emden problem in catalytic diffusion reactions

A new effective technique based on Chebyshev Finite Difference Method is introduced. First order smoothness of the approximation polynomial at the end points of each sub-interval is imposed in addition to the continuity condition. Both round-off and truncation error analyses are given besides the convergence analysis. Coupled Lane Emden boundary value problem in Catalytic Diffusion Reactions is investigated by using presented method. The obtained results are compared with the existing methods in the literature and it is observed that the proposed method gives more reliable results than the others.

Fractional Chebyshev Finite Difference Method for Solving the Fractional-Order Delay BVPs

In this paper, we implement an efficient numerical technique which we call fractional Chebyshev finite difference method (FChFDM). The fractional derivatives are presented in terms of Caputo sense. The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a nonuniform finite difference scheme. The error bound for the fractional derivatives is introduced. We used the introduced technique to solve numerically the fractional-order delay BVPs. The application of the proposed method to introduced problem leads to algebraic systems which can be solved by an appropriate numerical method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

On Solution of Fredholm Integrodifferential Equations Using Composite Chebyshev Finite Difference Method

A new numerical method is introduced for solving linear Fredholm integrodifferential equations which is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well-known Chebyshev-Gauss-Lobatto collocation points. Composite Chebyshev finite difference method is indeed an extension of the Chebyshev finite difference method and can be considered as a nonuniform finite difference scheme. The main advantage of the proposed method is reducing the given problem to a set of algebraic equations. Some examples are given to approve the efficiency and the accuracy of the proposed method.