Solving third-order boundary value problem by direct methods

In this research, the direct method of multistep method is developed for the numerical solution of nonlinear boundary value problems (BVPs) of Type 1 and Type 2 directly. Most of the existing research involving BVPs will reduce the problem to a system of first order Ordinary Differential Equations (ODEs). However, the proposed method will solve the third-order BVPs directly without reducing to first-order ODEs with constant step size using the shooting technique. On- point and two-point direct block method of Adam Moulton have been derived. These methods consists the predictor and corrector method where the predictor is one order less than the corrector. In the numerical results, one-point direct methods have advantages in accuracy and for two-point direct block methods have advantages in timing calculation. The results clearly show that the proposed method is suitable for solving third-order nonlinear BVPs.

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