Abstract:
For the solution of the Cauchy problem for the equation $$ u_{tt}=u_{xx}+i2u_{ttx}+u_{ttxx} $$ with discontinuous initial data, asymptotic formulas as $t\to\infty$ are derived, which agree well with numerical results. The stability of the numerical methods used is analyzed. Other results are presented concerning nonstandard linear equations produced by homogenizing the equations describing wave processes in periodic stratified media.
Key words:wave processes in periodic stratified media, nonstandard linear partial differential equations, Cauchy problem with discontinuous initial data, asymptotics of solutions at large $t$, saddle point method, stationary phase method, finite-difference method, matrix tridiagonal Gaussian elimination, stability, analytical computation system REDUCE.
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