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.