A P-Stable Linear Multistep Method For Solving General Third Order Ordinary Differential Equations

A P-stable linear multistep method for solving general third order initial value problems of ordinary differential equations without first reducing the problems into a system of first order equations is considered. The approach for the development of this method is essentially based on collocation of the differential system generated from a basis function. A predictor for the evaluation of $y_{n+k}$ for an odd $k\ge 3$ in the main method is also proposed. The two resulting methods, the corrector and the predictor are P-stable for $k = 3$ . These as a block are tested on a number of problems to show their efficiency. When the methods (the corrector and the predictor) are evaluated at $x = x_{n+3}$ identical schemes are obtained as special cases of the methods, while the set of first and second derivatives obtained from the corrector are different from those obtained from the predictor.

Keywords:

• Linear Multistep Method
• P-stable
• Third Order Ivps Of Odes
• Stiff And Non-stiff Initial Value Problems
• Corrector
• Predictor