A wavelet method for nonlinear variable-order time fractional 2D Schrödinger equation

In this study, an efficient semi-discrete method based on the two-dimensional Legendre wavelets (2D LWs) is developed to provide approximate solutions for nonlinear variable-order time fractional (2D) Schrödinger equation. First, derivative involved in considered problem approximated via finite difference technique. Then, by help of scheme and theta-weighted method, a recursive algorithm derived under examination. After that, real functions available imaginary parts unknown solution are expanded 2D LWs. Finally, applying operational matrices derivative, transformed linear system algebraic equations each step which can simply be solved. In proposed acceptable achieved employing only small number basis functions. To illustrate applicability, validity accuracy wavelet some numerical test examples solved using suggested method. The results reveal that established LWs very easy implement, appropriate accurate solving model.