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

Rationalized Haar functions (RHFs, for short) are applied for solving linear first- and second-order partial differential equations (PDEs, for short). For this purpose, new operational matrices of integration and differentiation based on a double rationalized Haar series are derived. By using these operational matrices for their solution, the PDEs are transformed into matrix equations quite easily. Coefficients of double rationalized Haar series related to their solutions can be obtained by solving these matrix equations. Some numerical examples are also included.