Abstract: Partial integral equation (PIE) representation of a partial differential equation (PDE) allows using computationally tractable algorithms for analysis, simulation, and optimal control.

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To demonstrate its practical application, the code solves a PDE derived from a predator-prey model. This model is renowned for generating solutions that exhibit Turing patterns, which are observed in ...

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various ...

Abstract: In this paper, a novel approach leveraging artificial neural networks is introduced to approximate solutions for partial differential equations. The one ...