Numerical analysis for fractional Bratu type equation with explicit and implicit methods

Abstract

Bratu‐type equation has wide applications in physics, finance, and other fields. Also, fractional analysis has been a popular topic recently. It is difficult to find the analytical solution once we add the fractional operator on the left side of the equation. In this work, we apply explicit and implicit finite difference methods to solve the fractional Bratu equation. From the numerical examples, we will see that the explicit solution is not accurate, and the implicit solution based on Newton's method is efficient in some sense. Some theoretical results are mentioned in the paper.