Numerical Solution of Stiff and Singularly Perturbed Problems. Numerical Solution of Stiff and Singularly Perturbed Problems for Ordinary Differential and Volterra-type Equations

      Аннотация: In recent years much attention has been given to the numerical solution of ODEs. Of particular interest has been the solution of singularly perturbed and stiff problems. These types of problems arise in various fields of science and engineering such as fluid mechanics, physics, chemistry, mechanics, chemical reactor theory, convection diffusion processes, optimal control and other branches of applied mathematics. Singular perturbation problems depend on the presence of a small, positive parameter which provides a multi-scale character to the solution. That is the solution varies very rapidly in some parts of the region of integration (layers) and varies slowly in other parts. Stiffness is a property of the differential problem that makes slow and expensive the computation of the numerical solution using classical explicit methods. In this work, we present some numerical methods for solving IVPs and BVBs. Moreover, we give numerical solutions of Volterra integral and integro-differential equations. This book is high recommended to both postgraduate students and researchers in a wide variety of applications.

Ключевые слова: ordinary differential equations, Boundary value problems, Singularly Perturbed Problems, Stiff problems, Initial Value Problems, Volterra Integral and Integro-differential Equations