GitHub

SciMLBenchmarks.jl: Benchmarks for Scientific Machine Learning (SciML) and Equation Solvers

SciMLBenchmarks.jl holds webpages, pdfs, and notebooks showing the benchmarks for the SciML Scientific Machine Learning Software ecosystem, including: Benchmarks of equation solver implementations ...
Scientific Research Publishing

An Efficient Explicit Scheme for Solving the 2D Heat Equation with Stability and Convergence Analysis ()

1 Department of Mathematical Sciences, Kent State University, Kent, OH, USA. 2 Department of Mathematics, Comilla University, Cumilla, Bangladesh. 3 School of Computer Science and Technology, ...
GitHub

Applied Partial Differential Equations

Learn how to classify PDEs,and apply and visualize characteristic and finite difference solution methods. You can use these live scripts as demonstrations in lectures, class activities, or interactive ...
PNAS

Bridging the gap between models based on ordinary, delayed, and fractional differentials equations through integral kernels

This study centers on incorporating memory effects (the impact of past events on current states) into mathematical models for population dynamics. It introduces a framework based on the gamma ...
IEEE

Numerical Solution of Second-Order Fredholm Integro-Differential Equations Using the Chebyshev Collocation Method

Abstract: This paper explores the reliability of the Chebyshev collocation Method (CCM) as a numerical approach used for solving a specific class of equations known as the second-order Fredholm ...
IEEE

An Offset-Cancelling Discrete-Time Analog Computer for Solving 1-D Wave Equations

Abstract: This article describes a single-chip analog computer for solving 1-D wave equations. The chip uses switched-capacitor (SC)-based fully differential analog circuits to build a discrete-time ...
PNAS

Efficient quantum algorithm for dissipative nonlinear differential equations

Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity ...
Scientific Research Publishing

Solution of a Nonlinear Delay Differential Equation Using Adomian Decomposition Method with Accelerated Formula of Adomian Polynomial ()

1 Department of Physics & Engineering Mathematics, Faculty of Engineering, Mansoura University, Mansoura, Egypt. 2 Department of Physics & Engineering Mathematics, Faculty of Engineering El-Mataria, ...