A Numerical Method for an Integro-Differential Equation with Memory in Banach Spaces: Qualitative Properties

2003 ◽  
Vol 41 (4) ◽  
pp. 1232-1241 ◽  
Author(s):  
E. Cuesta ◽  
C. Palencia
Keyword(s):  
Differential Equation ◽  
Numerical Method ◽  
Banach Spaces ◽  
Qualitative Properties ◽  
Integro Differential Equation ◽  
With Memory

scholarly journals An existence theorem for solutions of an integro-differential equation in Banach spaces

2012 ◽  
Vol 45 (4) ◽  
Author(s):  
Aldona Dutkiewicz
Keyword(s):  
Differential Equation ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Initial Value Problem ◽  
Initial Value ◽  
Measures Of Noncompactness ◽  
Integro Differential Equation ◽  
Local Solutions

AbstractThe paper contains an existence theorem for local solutions of an initial value problem for a nonlinear integro-differential equation in Banach spaces. The assumptions and proofs are expressed in terms of measures of noncompactness.

Multi-Asset Option Pricing Based on Exponential Lévy Process

2013 ◽  
Vol 380-384 ◽  
pp. 4537-4540
Author(s):  
Nan Liu ◽  
Mei Ling Wang ◽  
Xue Bin Lü
Keyword(s):  
Differential Equation ◽  
Fourier Transform ◽  
Option Pricing ◽  
Numerical Method ◽  
Martingale Measure ◽  
Esscher Transform ◽  
Equivalent Martingale Measure ◽  
Integro Differential Equation ◽  
Equivalent Martingale ◽  
The Fourier Transform

The multi-dimensional Esscher transform was used to find a locally equivalent martingale measure to price the options based on multi-asset. An integro-differential equation was driven for the prices of multi-asset options. The numerical method based on the Fourier transform was used to calculate some special multi-asset options in exponential Lévy models. As an example we give the calculation of extreme options.

scholarly journals On the Kneser-Hukuhara property for an integro-differential equation in Banach spaces

2011 ◽  
Vol 48 (1) ◽  
pp. 51-59
Author(s):  
Aldona Dutkiewicz
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Banach Spaces ◽  
Topological Properties ◽  
Measure Of Weak Noncompactness ◽  
Integro Differential Equation

Abstract In this paper we investigate some topological properties of solutions sets of some integro-differential equations in Banach spaces. Our assumptions and proofs are expressed in terms of the measure of weak noncompactness.

New approximation method for Volterra nonlinear integro-differential equation

2019 ◽  
Vol 12 (01) ◽  
pp. 1950016 ◽  
Author(s):  
Sami Segni ◽  
Mourad Ghiat ◽  
Hamza Guebbai
Keyword(s):  
Differential Equation ◽  
Numerical Method ◽  
Approximation Method ◽  
New Method ◽  
Integro Differential Equation ◽  
Numerical Tests

In this work, we build a new numerical method to approximate the solution of Volterra’s nonlinear integro-differential equation. This method needs fewer conditions to converge, compared to the direct Nytröm method. Numerical tests show its efficiency. This new method is more practical and compatible with the Volterra nonlinear integro-differential equation.

Sign in / Sign up

Export Citation Format

Share Document