Physics-aware machine learning integrates domain-specific physical knowledge into machine learning models, leading to the development of physics-informed neural networks (PINNs). PINNs embed physical ...

In this paper, the boundary value problems for second order singularly perturbed delay differential equations are treated. A generic numerical approach based on finite difference is presented to solve ...

Abstract: The existence and uniqueness of solutions of nonlinear fractional differential equations is the key point for stability theory and the design of feedback stabilization controllers. In this ...

Abstract: We consider the initial-boundary value problem governed by systems of linear hyperbolic partial differential equations in the canonical diagonal form and study conditions for exponential ...

This repository allows you to solve forward and inverse problems related to partial differential equations (PDEs) using finite basis physics-informed neural networks (FBPINNs). To improve the ...

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. Once a well-suited model is established, it can be thoroughly ...

In the realm of financial mathematics, differential equations play a pivotal role in modeling and solving problems related to various financial instruments and markets. These mathematical tools are ...

The method of stationary phase and the centred-difference approximation are used to generate the finite-difference scheme for solving Klein-Gordon equation in MATLAB. Solves initial value problem of ...

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If today's college students could find a way to get their hands on a copy of Facebook's latest neural network, they could cheat all the way through Calc 3. They could even solve the differential ...