Influence of stochastic disturbances on the quasi-wavelet solution of the convection–diffusion equation

Abstract

A quasi-wavelet numerical method (QWNM) is introduced for solving the convection–diffusion equation (CDE). The results manifest that the calculated bandwidth has an extremum. When the bandwidth takes the value of the extremum, the accuracy of the solution for the CDE by using the QWNM is relatively high and better than that by using the up-wind scheme. Under the condition of stochastic boundary disturbances of different amplitudes, the results of the QWNM are a little worse than those of the up-wind scheme when the integral time is longer. However, when stochastic boundary disturbances of equal amplitudes occur, the solutions of the equation by using the QWNM and the up-wind scheme can be identical if the bandwidth takes an integer greater than or equal to 20. When the parameter is stochastically disturbed, the root-mean-square error of the quasi-wavelet solution of the equation is smaller than that of the up-wind scheme solution if the bandwidth is 10. When the initial values are stochastically disturbed and the bandwidth equals 10, the accuracy of the quasi-wavelet solution is relatively high and better than that of the up-wind scheme solution.