This book is an invaluable resource for applied researchers to find the analytical solution of differential equations describing the dynamical system with less computational effort and time. It describes the basic concepts of the differential transform method and solution of various real-world problems described by simple to complicated differential equations. It provides a computational technique that is not only conceptually simple and easy to use but also readily adaptable for computer coding. Different chapters of the book deal with the basic differential equations involved in the physical phenomena as well as a complicated system of differential equations described by the mathematical model.
The book offers comprehensive coverage of the most essential topics, including
- Basic concepts and fundamental properties of the proposed technique with proof
- The solution of linear, nonlinear, homogeneous, and nonhomogeneous ordinary differential equations (ODEs) and partial differential equations (PDEs)
- The initial and boundary value problems
- Real-world ODE and PDE problems are also discussed
Applications of Differential Transform to Real World Problems is primarily aimed at undergraduates, graduates, and researchers studying differential equations. Scientists dealing with complicated differential equations or systems of differential equations will also find this book useful.
Preface. Authors. Chapter 1 One-Dimensional Differential Transform Method. Chapter 2 Application of the One-Dimensional Differential Transform Method to Solve Real-World Problems. Chapter 3 Solution of a System of Differential Equations by the One Dimensional Differential Transform Method. Chapter 4 A Coupled System of Ordinary Differential Equations–Based Real-World Problems and Its Solution by the One Dimensional Differential Transform Method. Chapter 5 Two-Dimensional Differential Transform Method. Chapter 6 Application of the Differential Transform Method to a System of Partial Differential Equations. Chapter 7 Solution of a Partial Differential Equation Describing Transport Phenomena by the Differential Transform Method. Chapter 8 A Compartment Model of the Reaction Diffusion Mechanism in Cell 42 and Its Solution Using the Differential Transform Method. Chapter 9 An Application of the Differential Transform Method to Solve Partial Differential Equation–Based Real-World Problems. Chapter 10 Analytical Solutions Using the Differential Transform Method and Their Convergence. Index.