Block Bi-Basis Collocation Method for Direct Approximation of Fourth-order IVP

Block Bi-Basis Collocation Method for

Abstract

This study presents the derivation of two-step fifth-order hybrid scheme based on the combination of Hermite and shifted Chebyshev polynomials as bases functions of the collocation techniques. The technique was used to generate a set of hybrid schemes at selected grid and non-grid points and implemented as a block method. The derived block method (Block Bi-basis Collocation Method) was applied as a simultaneous integrator to linear and non-linear fourth-order initial value problems of ordinary differential equations. The zero stability, order, error constants, consistency, convergence and numerical results of the proposed block method are analysed. The application of the block bi-basis collocation method to some fourth-order initial value problems demonstrated the effectiveness and accuracy of the method. The block bi-basis collocation method compared favorably with existing methods in literature.