Two-point diagonally implicit multistep block method for solving Robin boundary value problems using variable step size strategy

• Main Authors: Nadirah, Mohd Nasir, Zanariah, Abdul Majid, Fudziah, Ismail, Norfifah, Bachok
• Format: Article
• Language: English
• Published: Akademi Sains Malaysia 2019
• Subjects: QA Mathematics
• Online Access: http://umpir.ump.edu.my/id/eprint/32341/1/PAPER%202.pdf; http://umpir.ump.edu.my/id/eprint/32341/; https://www.akademisains.gov.my/asmsj/?mdocs-file=4149

This study focuses on the multistep integration method for approximating directly the solutions of the second order boundary value problems (BVPs) with Robin boundary conditions. The derivation of the predictor and corrector formulas uses Lagrange interpolation polynomial in the form of Adam's method. Two numerical solutions are computed concurrently within a block method with non-uniformly step size. The implementation of multistep block method follows the m PE(CE) procedure via shooting technique. Newton divided difference interpolation method is used during the iterative process for estimating the guessing values. The properties including the order, zerostable and stability region of the proposed method are discussed. Numerical examples are given to demonstrate the computational efficiency of the developed method.