Half-step numerical model of order ten for solution of first and second orders ordinary differential equations

Abstract

This paper concentrates on the derivation of new numerical model and its application to first and second orders initial value problems concurrently. This numerical technique was developed via interpolation and collocation approach using power series as interpolating polynomial. The first as well as second derivatives of this polynomial were taken as collocating equations which combined with the interpolation equation to form a system of nonlinear equations. Gaussian elimination technique was applied to these equations in order to find the unknown variables that were substituted into the interpolating polynomial to produce a continuous implicit scheme. The non-interpolating points within the interval of integration were evaluated to form the block method. The accuracy of the new developed numerical model was examined by solving some first and second orders initial values problems and results generated proved its efficiency over existing methods.

Subject Classification: (2010):

• 65L05
• 65L06
• 65L08

Keywords:

• Block method
• Collocation
• Hybrid
• Interpolation
• Power series