Finding numerical solution of linear partial differential equations of first order with real coefficients

Abstract

Applying Bittner's operational calculus we present a method to give approximate solutions of linear partial differential equations of first order $$\mathop \sum \limits_{i = 1}^n b_i \frac{{\partial u(x_1 ,x_2 , \ldots ,x_n )}}{{\partial x_i }} = f(x_1 ,x_2 , \ldots ,x_n )$$ with real coefficients and with condition $$u(x_1 ,x_2 , \ldots ,x_{n - 1,} x_n^0 ) = \varphi (x_1 ,x_2 , \ldots ,x_{n - 1,} ).$$