In the present work, the computer algebra system (CAS) is applied for constructing a new version of the analytic-numerical method of collocations and least residuals (CLR) for solving the Burgers equa- tion and the Korteweg-de Vries-Burgers equation. The CAS is employed at all stages from writing, deriving, and verifying the formulas of the method to their translation into arithmetic operators of the Fortran lan- guage. The verification of derived formulas of the method has been done on the test problem solutions. Comparisons of the results of numerical computations by the new CLR method with the exact solutions of test problems show a high accuracy of the developed method. and investigation of new numerical algorithms. The method of collocations and least squares (CLS) was originally developed for the numerical solution of stationary problems of fluid dynamics. In the work (39), this method was applied for the numerical solution of the Stokes equations of viscous incompressible fluid. The CLS method was extended in (38) for the case of the numerical solution of two-dimensional Navier-Stokes equations of viscous incompressible fluid, and a square computational grid was used in the plane of two spatial coordinates. The CLS method was generalized in (19, 20) for the case of rectangular grid cells in the two-dimensional case. The versions of the CLS method with the accuracy orders from 2 to 8 were developed in (20), � The work was partially supported by the Russian Foundation for Basic research
['V. P. Shapeev', 'Evgenii V. Vorozhtsov']
CAS Application to the Construction of the Collocations and Least Residuals Method for the Solution of the Burgers and Korteweg–de Vries–Burgers Equations