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This work presents a fast and efficient approach for solving the Fokker–Planck equation via the Laguerre wavelet collocation method. Properties of the Laguerre wavelet are presented, along with the Laguerre basis to reduce the problems into systems of either linear or nonlinear algebraic equations. This system is then solved to find the unknown coefficients. A convergent analysis for the proposed scheme is explained through theorems. Several numerical examples are presented to demonstrate the applicability and accuracy of the method to a wide variety of similar problems. The results are compared to other methods through graphs and tables. [ABSTRACT FROM AUTHOR]

In this article, we proposed an efficient numerical technique for the solution of fractional-order (1 + 1) dimensional telegraph equation using the Laguerre wavelet collocation method. Some examples are illustrated to inspect the efficiency of the proposed technique and convergence analysis is discussed in terms of a theorem. Here, the fractional-order telegraph equation is converted into a system of algebraic equations using the properties of the Laguerre wavelet, and solutions obtained by the proposed scheme are more accurate and they are compared with the analytical solution and other method existed in the literature. [ABSTRACT FROM AUTHOR]