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, Improved Residual Power Series Method (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.

• Explores the application of Improved Residual Power Series Method (IRPSM) to a wide range of problems, including ordinary and partial differential equations, multi-point BVPs, and complex systems in physics and engineering

• Highlights Improved Residual Power Series Method (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 like fluid dynamics and engineering

• Provides Mathematica codes for each solved problem, allowing readers to understand the solution procedure and implement Improved Residual Power Series Method (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