The depth-averaged hydrodynamic equations were numerically investigated. Numerical solutions of the obtained using Chebyshev polynomials for a given number operations and various ratios layers polynomials.Numerical compared with analytical ones using, as an example, heat conduction equation. performed numerical studies demonstrated tendency solution to exact one over time in all cases considere...

Differential models, numerical methods and computer simulations play a fundamental role in applied sciences. Since most of the differential models inspired by real world applications have no analytical solutions, development efficient simulation algorithms key computation solutions to many relevant problems. Moreover, since model parameters mathematical interesting scientific interpretations th...