Sujaul Chowdhury, Syed Badiuzzaman Faruque, Ponkog Kumar Das
Numerical Solutions of Boundary Value Problems of Non-linear Differential Equations
Numerical Solutions of Boundary Value Problems of Non-linear Differential Equations
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- More about Numerical Solutions of Boundary Value Problems of Non-linear Differential Equations
The book provides numerical solutions to non-linear differential equations by replacing derivatives with finite difference approximations and solving the resulting system of non-linear algebraic equations using Newtons iterative method. Euler solutions are also obtained and convergence to Euler solutions is verified.
Format: Hardback
Length: 100 pages
Publication date: 25 October 2021
Publisher: Taylor & Francis Ltd
The book offers in-depth and comprehensive coverage of numerical solutions to boundary value problems involving a diverse range of non-linear differential equations. By employing finite difference approximations in these differential equations, we transform them into a system of non-linear algebraic equations. Through the use of Newtons iterative method, we successfully solve this system, obtaining both Euler solutions and confirming that the iterations converge towards Euler solutions. Interestingly, we discovered that, except for the boundary values, the initial values of the 1st iteration need not be closely related to the final convergent values of the numerical solution. To obtain these numerical solutions, we developed programs in Mathematica 6.0.
Dimension: 216 x 138 (mm)
ISBN-13: 9781032069951
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