Linear Block Method Derived from Direct Taylor Series Expansions for Solving Linear Third Order Boundary Value Problems

摘要

One of the conventional approaches for developing linear multistep method (LMM) for solving ordinary differential equations (ODEs) is the Taylor series expansions approach. Although this approach has not gained much attention in literature in comparison to its interpolation and numericalintegration counterparts. The Taylor series expansions approach could also be adapted for developing linear block methods with the introduction of new required expressions to obtain the resulting block method. This linear block method directly approximates the numerical solution of third orderODEs without going through the rigour of reduction to a system of first order ODEs. Therefore, this article defines a general form of linear block methods for solving third order boundary value problems with the unknown coefficients in the block method obtained from direct Taylor series expansions.The basic properties of the resulting linear block method are investigated where the block method satisfies the convergence criteria. In addition, the linear block method is implemented to solve linear boundary value problems with better accuracy in comparison to other numerical approachesin literature.