Solving systems of linear differential equations by Walsh polynomials approach

Abstract. György Gát and the author of this paper established a procedure to solve initial value problems of linear differential equations of first-order with not necessary constant coefficients. This procedure approximates the exact solution by Walsh polynomials. This paper extends this method for systems of linear differential equations of first-order with discontinuous righthand sides.

Key words and phrases. Fourier analysis, Walsh—Paley system, numerical solution of linear differential equations, triangular functions, uniform convergence, differential equations with discontinuous righthand sides.