Penyelesaian terus persamaan pembezaan biasa peringkat tiga menggunakan kaedah blok hibrid kolokasi diperbaiki

Abstract

The improved block hybrid collocation method (KBHK(B)) with two off-step points and four collocation points is proposed for the direct solution of general third order ordinary differential equations. Modification is done by adding first derivative of third order function into the general form of block hybrid collocation method to yield KBHK(B). Both main and additional methods are derived via interpolation (power series function) and collocation of the basic polynomial. An improved block method is derived to provide the approximation at five points concurrently. Zero stability, consistency, convergence and absolute stability region of KBHK(B) are investigated. Some numerical examples with exact solution are tested to illustrate the efficiency of the method. KBHK(B) is compared by other block hibrid collocation method in term of global error and step number. It is shown that KBHK(B) generates minimum global error with minimum step number.