This book contains twenty chapters and covers methods that may be used for solving different linear as well as nonlinear ordinary and partial differential equations (ODEs and PDEs). Chapter 1 begins with a review of basic numerical methods. Chapters 2 and 3 deal with Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced in Chapter 4. Then, in Chapters 5 to 8, the authors discuss Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), as well as Boundary Element Method (BEM). These topics are considered respectively to have first-hand experience for solving simple differential equations. In Chapters 9 and 10, analytical/semi analytic methods, namely, Akbari Ganji’s Method (AGM) and Exp-function, are used for solving nonlinear differential equations. Next, the nonlinear differential equations are addressed using Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Homotopy Analysis Method (HAM) in Chapters 11 to 14. Further, emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach are considered in Chapters 15 and 16. Chapter 17 consists of a few combined forms of the above mentioned methods or the hybrid methods for solving differential equations. Chapters 18 and 19 discuss the groundwork related to uncertain differential equations and geometric approach method for solving linear systems of uncertain differential equations. Finally, Chapter 20 covers the interval finite element method.
