Wavelet Adaptive Method For Solving Fractional Partial Differential Equations

In this paper, we consider the wavelet adaptive methods for solving fractional partial differential equations. Due to the non-Locality characteristic of fractional operators, the solutions for the fractional differential equations require a large amount of com-putation. For a class of problems which containing the local structure, the adaptive approach compared with the uniform method tends to a great of advantage.We use the magnitude of the wavelet approximation coefficients to design an adaptive algorithm, which dynamically adjust the location and number of basis functions, ensuring the accuracy and significantly reducing the computational cost. These algorithms are simple, some numerical examples are given to verify their validity.