A New Numerical Method for Fast Solution of Partial Integro-Differential Equations
This method offers a significant computational speedup for solving differential equations, which is important for researchers and engineers in computational science.
The paper proposes a new numerical method for solving partial integro-differential equations that achieves linear growth in operations with grid size, compared to quadratic growth in standard methods, as demonstrated on the 2D Poisson equation.
A new method of numerical solution for partial differential equations is proposed. The method is based on a fast matrix multiplication algorithm. Two-dimensional Poison equation is used for comparison of the proposed method with conventional numerical methods. It was shown that the new method allows for linear growth in the number of elementary addition and multiplication operations with the growth of grid size, as contrasted with quadratic growth necessitated by the standard numerical methods. The proposed method can be easily generalized for any differential equations.