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Russian mathematician finds new approach to 190-year-old 'eternal' math problem

A Russian mathematician has developed a new method for analyzing a class of equations that underpin models in physics and economics and are considered "eternal" as they have challenged researchers for ...
Frontiers

Unveiling new insights: taming complex local fractional Burger equations with the local fractional Elzaki transform decomposition method

This study aims to address the difficulties in solving coupled generalized non-linear Burger equations using local fractional calculus as a framework. The methodology used in this work, particularly ...
IEEE

Solution of piecewise-linear ordinary differential equations using waveform relaxation and Laplace transforms

Abstract: Piecewise-linear (PWL) functions are frequently used to describe the nonlinear branch equations of nonlinear devices in LSI circuits. New techniques for the solution of the differential ...
GlobalSpec

Basics of the finite difference method for solving the 2D Laplace equation

Heat energy plays an essential role in numerous engineering applications, from thermal management in electronic devices to the design of efficient energy systems. Understanding and predicting the ...
C&EN

Calculation of the Meniscus Shape Formed under Gravitational Force by Solving the Young–Laplace Differential Equation Using the Bézier Curve Method

Department of Chemical and Biological Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, OntarioK1N 6N5, Canada ...
Scientific Research Publishing

Laplace Transform, Non-Constant Coefficients Differential Equations and Applications to Riccati Equation ()

In this paper, the Laplace Transform is used to find explicit solutions of a fam-ily of second order Differential Equations with non-constant coefficients. For some of these equations, it is possible ...