Learn about the definitions, pros, cons, examples, and tips for choosing between explicit and implicit numerical methods for solving mathematical problems.

Learn the difference, pros, and cons of explicit and implicit numerical methods, and how to choose the best one for your mechanical engineering problem.

Summary form only given. The evolution of a short, intense laser pulse propagating in an underdense plasma is of particular interest for laser-plasma accelerator physics. This case is well-modeled by ...

Numerical integration, or time domain simulation, is an important tool to study dynamical systems. Many dynamical systems are stiff, for instance, electric power systems consist of a variety of ...

Abstract Interest in the construction of efficient methods for solving initial value problems that have some peculiar properties with it or its solution is recently gaining wide popularity. Based on ...

The Heat Equation Solver project provides a comprehensive analysis of the Heat Equation's numerical solutions using both the Explicit and Implicit methods. It demonstrates the trade-offs between ...

This paper analyzes the shortcomings of this approach, and proposes to apply explicit numerical schemes with stability control on the integration step and with reduction of some of state variables. A ...

Carl A. Rouse, A Method for the Numerical Calculation of Hydrodynamic Flow and Radiation Diffusion by Implicit Differencing, Journal of the Society for Industrial and Applied Mathematics, Vol. 9, No.

STABILITY AND ERROR ESTIMATES OF LOCAL DISCONTINUOUS GALERKIN METHODS WITH IMPLICIT-EXPLICIT TIME-MARCHING FOR ADVECTION-DIFFUSION PROBLEMS HAIJIN WANG, CHI-WANG SHU and QIANG ZHANG SIAM Journal on ...