Introduction to Numerical Methods for Time Dependent Differential Equations

<p><b>Introduces both the fundamentals of time dependent differential equations and their numerical solutions</b></p> <p><i>Introduction to Numerical Methods for Time Dependent Differential Equations </i>delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs).</p> <p>Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the theory of scalar equations, finite difference approximations, and the Explicit Euler method. Next, a discussion on higher order approximations, implicit methods, multistep methods, Fourier interpolation, PDEs in one space dimension as well as their related systems is provided.</p> <p><i>Introduction to Numerical Methods for Time Dependent Differential Equations </i>features:</p> <ul> <li>A step-by-step discussion of the procedures needed to prove the stability of difference approximations</li> <li>Multiple exercises throughout with select answers, providing readers with a practical guide to understanding the approximations of differential equations</li> <li>A simplified approach in a one space dimension</li> <li>Analytical theory for difference approximations that is particularly useful to clarify procedures</li> </ul> <p><i>Introduction to Numerical Methods for Time Dependent Differential Equations </i>is an excellent textbook for upper-undergraduate courses in applied mathematics, engineering, and physics as well as a useful reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs or predict and investigate phenomena from many disciplines.</p>