Abstract: In this paper, a novel approach leveraging artificial neural networks is introduced to approximate solutions for partial differential equations. The one ...

The nonlinear Riccati differential equation, since its enunciation by Jacopo Riccati in 1724, has become a legendary equation. Despite a 300-year search for a solution, it has not been possible to ...

Instituto Nacional de Investigaciones Nucleares, Centro Nuclear de México, Departamento de Física, City La Marquesa Ocoyoacac, Estado de México, Mexico. Nonlinear differential equations are often ...

Abstract: A nonlinear equation system often has multiple roots, while finding all roots simultaneously in one run remains a challenging work in numerical optimization. Although many methods have been ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

A direct power series substitution technique is proposed to solve second order nonlinear differential equations. The errors in truncated power series are estimated to determine the significance of the ...