# Numerical algorithm for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term

## TL;DR

This paper develops an ADI difference scheme for solving a complex two-dimensional time-fractional wave equation with distributed order and nonlinear source, ensuring stability, convergence, and verified accuracy through numerical tests.

## Contribution

It introduces a novel ADI difference scheme for a complex fractional wave equation with distributed order and nonlinear source, analyzing its stability and convergence.

## Key findings

- The scheme is unconditionally stable.
- The method achieves high accuracy in numerical experiments.
- Numerical results confirm the effectiveness of the proposed algorithm.

## Abstract

In this paper, an alternating direction implicit (ADI) difference scheme for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term is presented. The unique solvability of the difference solution is discussed, and the unconditional stability and convergence order of the numerical scheme are analysed. Finally, numerical experiments are carried out to verify the effectiveness and accuracy of the algorithm.