SOME ANALYTICAL METHODS FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS

Mathematics

In recent years there has been an explosion of interest in the study of numerical methods for solving nonlinear Partial Differential Equations (PDEs) describing nonlinear wave phenomena with the results often motivated by the use of computers. These equations are difficult to analyze mathematically. The modeling has witnessed major progress in recent years in terms of new methods, modifications, resolved problems and the range of applications. A variety of analytical, asymptotic and numerical models have been developed over the past few decades to provide a framework for understanding the wave phenomena describing In this paper, we present a comprehensive literature review of shock waves and various semi-analytical/ numerical methods in finding solution. We also present limitations in the present research work and scope for future work.

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