Solution of the Burgers Equation in the Time Domain

Solution of the Burgers Equation in the Time Domain

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This paper deals with a theoretical description of the propagation of a finite amplitude acoustic waves.The theory based on the homogeneous Burgers equation of the second order of accuracy is presented here.This read more equation takes into account both nonlinear effects and dissipation.The method for solving this equation, using the well-known Cole-Hopf transformation, is presented.

Two methods for numerical solution of these equations in the time domain are presented.The first is based on the simple Simpson method, which is suitable for smaller Goldberg numbers.The second uses the more advanced skull bride and groom saddle point method, and is appropriate for large Goldberg numbers.