Multistep block method for solving second and third order boundary value problems with Robin and mixed type boundary conditions

This thesis investigates on the numerical solutions for solving two-point and multipoint boundary value problems (BVPs) subject to Robin and mixed boundary conditions. The BVPs are solved directly using the new developed two-point diagonally implicit multistep block method in the form of Adams type formula. Constant and variable step size strategy are employed for solving two-point second-order BVPs. Meanwhile, the computed solutions for two-point and multipoint third-order BVPs are limit to constant step size. Shooting technique is implemented in order to solve the BVPs. The initial estimate values are obtained using the Newton’s divided difference interpolation method and Steffensen’s method. Alternatively, the first derivative function is absence during the calculation of guessing values compared to the shooting technique via the Newton’s method. The analysis included order, error constants, consistency, zero-stability and convergence are presented in describing the characteristics of the proposed methods. All the computational procedures were undertaken using the C language in a Code::Blocks 16.01 cross platform. Numerical results showed significant findings where the proposed methods could offer better accuracy results, less costly in terms of total function calls and faster in timing compared to the existing methods. In conclusion, the proposed methods and developed algorithms were shown to be a reliable BVPs solver for solving two-point and multipoint BVPs subject to Robin and mixed boundary conditions directly.

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