Traveling Wave Analysis of Partial Differential Equations

The book explores the intersection of numerical methods and analytical solutions in the context of Partial Differential Equations (PDEs). It highlights the necessity of testing and validating numerical methods against PDEs with known solutions. Recent advancements in analytical solutions, especially traveling wave solutions for nonlinear evolutionary PDEs, are emphasized as crucial for developing robust numerical methods. This synergy between analytical research and numerical validation creates a rich framework for evaluating and enhancing computational techniques in PDE analysis.