Abstract
This study is intended to evaluate numerically the solution of second order boundary value problems (BVPs) subject to mixed boundary conditions using a direct method. The mixed set of boundary conditions is subsumed under Type 1: mixed boundary conditions of Dirichlet and Robin and Type 2: mixed boundary conditions of Robin and Neumann. The direct integration procedure will compute the solutions at two values concurrently within a block with a fixed step size. The shooting technique adapted to the derivative free Steffensen method is employed as the iterative strategy to generate the new initial estimates. Four numerical examples are given to measure the efficiency and effectiveness of the developed numerical scheme of order six. The computational comparison indicates that the proposed method gives favorably competitive performance compared to the existing method in terms of accuracy, total function calls, and time saving.
Highlights
The essential role of numerical analysis is to give good insight to a practitioner to find the approximate solutions, especially when an exact solution is required, but is very difficult to obtain.This can be done using a variety of numerical techniques as an alternative to an analytical method.In the beginning, the physical applications will be transformed into a mathematical model in differential equation form before being solved numerically
The physical applications will be transformed into a mathematical model in differential equation form before being solved numerically
The differential equations can be expressed as initial or boundary value problems that are subject to the initial conditions for the former type and boundary conditions for the latter type that governs the mathematical model
Summary
The essential role of numerical analysis is to give good insight to a practitioner to find the approximate solutions, especially when an exact solution is required, but is very difficult to obtain.This can be done using a variety of numerical techniques as an alternative to an analytical method.In the beginning, the physical applications will be transformed into a mathematical model in differential equation form before being solved numerically. The essential role of numerical analysis is to give good insight to a practitioner to find the approximate solutions, especially when an exact solution is required, but is very difficult to obtain. This can be done using a variety of numerical techniques as an alternative to an analytical method. The physical applications will be transformed into a mathematical model in differential equation form before being solved numerically. The differential equations can be expressed as initial or boundary value problems that are subject to the initial conditions for the former type and boundary conditions for the latter type that governs the mathematical model. Its importance has brought researchers to focus actively on an investigation that involves the improvement of their numerical scheme for solving two point boundary value problems (BVPs), giving a notable contribution for a more accurate result
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