Research On Construction Methods Of Two Types Numerical Formats

In many fields of mathematics,physics,and engineering technology,partial differential equations play a very important role and are main tools for solving problems.However,it is difficult to calculate the analytical solutions of most PDEs,so people focus on how to solve the numerical solution of PDEs.In order to construct a high-precision numerical format,people often increase the number of approximate values of solutions at discrete nodes in the equations of the format.However,this will cause problems such as a large amount of computer calculation and a long calculation time.With the popularization of computers,people began to use multiple computers to perform simultaneous operations to complete a problem,which greatly promoted the research of parallel algorithms,which made it very important to study the parallel operation of numerical solutions of partial differential equations.The following is the innovative work of this article.1.The Lawrie Sameh algorithm is used to provide a theory for studying parallel operations.For the Dirichlet problem of the equation,a variable limit integral method is used to construct a numerical format convenient for parallel algorithms.2.Using the equation itself,a corresponding transformation of the multivariate Taylor expansion of the solution is made,and the method of constructing explicit and implicit schemes is obtained by taking the independent variables for regional integration and line integration.The numerical discrete method of the nonlinear Kd V-Burgers equation is obtained by using the variable limit integral method combined with the Taylor formula and the Lagrange interpolation numerical fitting method.The uniqueness of the solution and the decreasing energy of the numerical discrete format are proved.Finally,numerical experiments verify the validity of the given numerical format.