Boundary value problems solving method with the implicit use of the Taylor expansions

Grid method for boundary value problems solving for partial differential equations based on high order Taylor expansions is suggested. Comparison of the proposed method with classical grid method is implemented. It is shown that the use of the Taylor expansion with specified partial differential equations allows to reduce the estimated faulty proportion of the numerical solution for a given constant sampling area by increasing the order of the expansion. A number of model boundary value problems is solved, the results of the estimated faulty proportion are given.