Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets

Abstract EN

A collocation method based on the second kind Chebyshev wavelets is proposed for the numerical solution of eighth-order two-point boundary value problems (BVPs) and initial value problems (IVPs) in ordinary differential equations.

The second kind Chebyshev wavelets operational matrix of integration is derived and used to transform the problem to a system of algebraic equations.

The uniform convergence analysis and error estimation for the proposed method are given.

Accuracy and efficiency of the suggested method are established through comparing with the existing quintic B-spline collocation method, homotopy asymptotic method, and modified decomposition method.

Numerical results obtained by the present method are in good agreement with the exact solutions available in the literatures.