Nature

Innovative Aboodh-based gractional analytical methods for nonlinear Burgers’ partial differential equations

This paper explores advanced analytical techniques for solving Burgers’ fractional partial differential equations (PDEs). We focus on the application of two innovative methods: the Aboodh transform ...
Nature

Wavelets based physics informed neural networks to solve non-linear differential equations

Physics informed neural networks (PINNs), a type of machine learning approach, can be used to find the solution of differential equations by including all of the physics into the loss function and ...
Scientific Research Publishing

Reproducing Kernel Hilbert Space Technique for Fourth-Order Singular Boundary Value Problems ()

Reproducing kernel Hilbert space method is utilized in this paper as an efficient approach to solve singular fourth order ...
Oil

Hydrodynamic equations model mud-pulse telemetry transmissions

A closed-loop drilling system, to be effective, requires reliable two-way communication between the downhole module and surface. 1 2 Today's drilling industry uses mud-pressure pulse telemetry as one ...