Approximation of Solutions to the Boundary Value Problems for the Generalized Boussinesq Equation

The paper is devoted to one of the Sobolev type mathematical models of uid ltration in a porous layer. Results that allow to obtain numerical solutions are signi cant for applied problems. We propose the following algorithm to solve the initial-boundary value problems describing the motion of a free surface ltered in a uid layer having nite depth. First, the boundary value problems are reduced to the Cauchy problems for integrodi erential equations, and then the problems are numerically integrated. However, numerous computational experiments show that the algorithm can be simpli ed by replacing the integro-di erential equations with the corresponding approximating Riccati di erential equations, whose solutions can also be found explicitly. In this case, the numerical values of the solution to the integro-di erential equation are concluded between successive values of approximating solutions. Therefore, we can pointwise estimate the approximation errors. Examples of results of numerical integration and corresponding approximations are given.