High-Accuracy Methods for Singular Perturbation Problems: Fourth-Order Adaptive Cubic Spline and Variable Mesh Schemes for Solving Singular Perturbation Problems

Mamatha, K.; Phaneendra, K.

ISBN 10: 6203925195 / ISBN 13: 9786203925197

Published by LAP LAMBERT Academic Publishing, 2025

About this Item

Seller Inventory # I-9786203925197

Bibliographic Details

• Title: High-Accuracy Methods for Singular Perturbation Problems: Fourth-Order Adaptive Cubic Spline and Variable Mesh Schemes for Solving Singular Perturbation Problems
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2025
• Language: English
• ISBN 10: 6203925195
• ISBN 13: 9786203925197
• Binding: Soft cover
• Condition: New

About this title

Synopsis

This book presents efficient numerical strategies for solving singular perturbation problems, particularly focus on differential-difference equations involving small delay parameters. Singular perturbation problems in various fields of engineering and applied sciences such as fluid dynamics, elasticity, quantum mechanics, electrical networks, are known for their boundary layer behavior, which challenges conventional numerical methods. This book reviews the theoretical background and existing literature before introducing two high-accuracy techniques: a Fourth-Order Adaptive Cubic Spline Method and a Variable Mesh Scheme. These methods are rigorously analyzed for stability, convergence, accuracy and are validated through extensive numerical experimentation. The work is motivated by the limitations of classical techniques and addresses the growing demand for robust computational methods in fields such as fluid dynamics, quantum mechanics, and reaction- diffusion process.