Abstract: The simulation of carrier transport in power electronic devices imposes stringent requirements on numerical stability, confining the previous methods to low-order schemes. To address this ...

A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, such ...

This course provides an introduction to topics involving ordinary differential equations. Emphasis is placed on the development of abstract concepts and applications for first-order and linear ...

1 College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, China. 2 School of Statistics and Data Science, Jiangxi University of Finance and Economics, Nanchang, China.

This is a Julia package for fractional differential equations and ODEs. It provides numerical solutions for nonlinear fractional ordinary differential equations (in the sense of Caputo). Related work ...

Abstract: This paper introduces two novel methods for solving multi-order fractional differential equations using Bernstein polynomials. The first method, referred to as the fractional operational ...

The fractional-order nonlinear Gardner and Cahn–Hilliard equations are often used to model ultra-short burst beams of light, complex fields of optics, photonic transmission systems, ions, and other ...

This paper presents a parameter-uniform numerical method to solve the time dependent singularly perturbed delay parabolic convection-diffusion problems. The solution to these problems displays a ...