An Implicit Collocation Method for Direct Solution of Fourth Order Ordinary Differential Equations

This paper presented a linear multistep method for solving fourth order initial value problems of ordinary differential equations. Collocation and interpolation methods are adopted in the derivation of the new numerical scheme which is further applied to finding direct solution of fourth order ordinary differentiation equations. This implementation strategy is more accurate and efficient than Adams–Bashforth Method solution. The newly derive scheme have better stabilities properties than that of the Adams-Bashforth Method. Numerical examples are included to illustrate the reliability and accuracy of the new methods.

Keywords
Linear Multistep Methods; Region of Absolute Stability; Zero-Stability; Error Analysis; Collocation.