A mathematician at Carnegie Mellon University has developed an easier way to solve quadratic equations. The mathematician hopes this method will help students avoid memorizing obtuse formulas. His ...

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...

Many dynamic processes can be described mathematically with the aid of stochastic partial differential equations. Scientists have found a new method which helps to solve a certain class of such ...

Abstract: In this paper, we propose a tensor multigrid method and an iterative tensor multigrid method to solve the Sylvester tensor equations which may arise from the discretization of high order ...

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 ...

In this study, we applied the variational iteration method to solve the Boussinesq time equation. Bossiness’s article from 1872 introduced the equations that are now known as the Boussinesq equations.

In this paper, we are going to present a class of nonlinear equation solving methods. Steffensen’s method is a simple method for solving a nonlinear equation. By using Steffensen’s method and by ...

In this article, we construct exact traveling wave solutions of the loaded Korteweg-de Vries, the loaded modified Korteweg-de Vries, and the loaded Gardner equation by the functional variable method.