This repository contains the implementation of a Physics-Informed Neural Network (PINN)-Enhanced Finite Difference Method (FDM) for modeling energy balance in hydraulic fracture propagation. The ...

We analyze finite difference methods for the Gross-Pitaevskii equation with an angular momentum rotation term in two and three dimensions and obtain the optimal convergence rate, for the conservative ...

The project employs an adaptive finite element method with a posteriori error estimation for solving boundary value problems of the form: -u''(x) + m * u'(x) + n * u ...

This is a preview. Log in through your library . Abstract A correction for truncation errors associated with implicit finite difference method (FDM) of the groundwater transport equation with reaction ...

A new approach in the finite difference framework is developed, which consists of three steps: choosing the dimension of the local approximation subspace, constructing a vector basis for this subspace ...

ABSTRACT: In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are ...