An application of rationalized Haar functions to solution of linear differential equations

Rationalized Haar functions (RHF´s) [1]-[5] are applied for solving linear differential equations (LDE´s). In this algorithm, the first derivatives of the solutions of LDE´s are expanded into rationalized Haar series with unknown coefficients. It is because an integration of a rationalized Haar approximation of its derivative in terms of time variable yields a piecewise-linear approximation (PWLA) of the solution. In a process of the solution, the given LDE´s are rewritten in the RHF system and are expressed in a form of matrix equations. The PWLA´s of the solutions can be obtained by using solutions of their matrix equations. In such a case, coefficient values of the PWLA´s can be efficiently computed along flowgraphs for inverse fast rationalized Haar transforms.