Short description:

This book introduces a semi-analytical method, Improved Residual Power Series Method (IRPSM) for solving boundary value problems (BVPs). Unlike traditional numerical and analytical techniques, IRPSM offers quick convergence and minimal computational time.

Long description:

This book introduces a semi- analytical method, Improved Residual Power Series Method (IRPSM), for solving boundary value problems (BVPs). Unlike traditional numerical and analytical techniques, IRPSM offers quick convergence and minimal computational time, avoiding the pitfalls of round- off errors, linearization, perturbation, and discretization. This innovative approach has been rigorously compared with existing methods, demonstrating superior accuracy and efficiency. The book is meant for scholars, researchers, and students in mathematics, engineering, and physics.

This book:

• Explores the application of IRPSM to a wide range of problems, including ordinary and partial differential equations, multi- point BVPs, and complex systems in physics and engineering


• Highlights IRPSM for its ability to efficiently handle highly nonlinear and complex boundary value problems, providing accurate solutions with reduced computational effort


• Demonstrates the method?s applicability across disciplines such as fluid dynamics and engineering


• Provides Mathematica codes for each solved problem, allowing readers to understand the solution procedure and implement IRPSM in their own research


• Offers a new and efficient method for solving BVPs and a practical reference for those seeking to minimize computational time and error in their work.

Table of Contents:

1. Basic Idea of the Improved Residual Power Series Method 2. IRPSM for the Solution of Two- and Multi-Points Boundary Value Problems 3. IRPSM for the Solution of Partial Differential Equations with Boundary Value Problems 4. IRPSM for the Solution of System of ODEs and PDEs with Boundary Value Problems 5. Application of IRPSM for Singularly Perturbed and Singularly Perturbed Delay Differential Equations 6. IRPSM for Heat Transfer Boundary Value Problems 7. IRPSM for Finite Boundary Value Problems in Fluid Dynamics