Volterra Integral Equation Approach to the Electron Dynamics in Intense Optical Pulses

2021 ◽  
pp. 41-63
Author(s):  
Yosuke Kayanuma
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Equation Approach ◽  
Electron Dynamics ◽  
Optical Pulses ◽  
Integral Equation Approach

Numerical solution of fractional differential equations via a Volterra integral equation approach

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Shahrokh Esmaeili ◽  
Mostafa Shamsi ◽  
Mehdi Dehghan
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Volterra Integral Equation ◽  
Equation Approach ◽  
Algebraic Equations ◽  
Integral Equation Approach ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
The Given

AbstractThe main focus of this paper is to present a numerical method for the solution of fractional differential equations. In this method, the properties of the Caputo derivative are used to reduce the given fractional differential equation into a Volterra integral equation. The entire domain is divided into several small domains, and by collocating the integral equation at two adjacent points a system of two algebraic equations in two unknowns is obtained. The method is applied to solve linear and nonlinear fractional differential equations. Also the error analysis is presented. Some examples are given and the numerical simulations are also provided to illustrate the effectiveness of the new method.

AN INTEGRAL EQUATION APPROACH TO PHASE TRANSITIONS IN FERROFLUIDS

1988 ◽  
Vol 49 (C8) ◽  
pp. C8-1847-C8-1848
Author(s):  
G. A. R. Martin ◽  
A. Bradbury ◽  
R. W. Chantrell
Keyword(s):  
Integral Equation ◽  
Phase Transitions ◽  
Equation Approach ◽  
Integral Equation Approach
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