Numerical Solution of Semilinear Integrodifferential Equations of Parabolic Type with Nonsmooth Data

1989 ◽  
Vol 26 (6) ◽  
pp. 1291-1309 ◽  
Author(s):  
Marie-Noëlle Le Roux ◽  
Vidar Thomée
Keyword(s):  
Numerical Solution ◽  
Parabolic Type ◽  
Integrodifferential Equations ◽  
Nonsmooth Data

On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order

2020 ◽  
Vol 26 (2) ◽  
pp. 263-272
Author(s):  
S. I. Unhale ◽  
Subhash D. Kendre
Keyword(s):  
Numerical Solution ◽  
Fractional Order ◽  
Integrodifferential Equation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Integrodifferential Equations ◽  
Successive Approximation Method ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

AbstractThe objective of this work is to study the local existence, uniqueness, stability and other properties of solutions of iterative mixed integrodifferential equations of fractional order. The Successive Approximation Method is applied for the numerical solution of iterative mixed integrodifferential equations of fractional order.

scholarly journals Stability Analysis of One-Leg Methods for Nonlinear Neutral Delay Integrodifferential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Yuexin Yu ◽  
Liping Wen
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Analytical Solution ◽  
Global Stability ◽  
Numerical Solution ◽  
Integrodifferential Equations ◽  
Neutral Delay ◽  
Numerical Tests ◽  
Theoretical Results

This paper is concerned with the numerical solution of nonlinear neutral delay integrodifferential equations (NDIDEs). The adaptation of one-leg methods is considered. It is proved that anA-stable one-leg method can preserve the global stability and a stronglyA-stable one-leg method can preserve the asymptotic stability of the analytical solution of nonlinear NDIDEs. Numerical tests are given to confirm the theoretical results.

scholarly journals Double Discretization Difference Schemes for Partial Integrodifferential Option Pricing Jump Diffusion Models

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
M.-C. Casabán ◽  
R. Company ◽  
L. Jódar ◽  
J.-V. Romero
Keyword(s):  
Option Pricing ◽  
Numerical Solution ◽  
Jump Diffusion ◽  
Spatial Domain ◽  
Diffusion Models ◽  
Explicit Scheme ◽  
Integrodifferential Equations ◽  
Difference Schemes

A new discretization strategy is introduced for the numerical solution of partial integrodifferential equations appearing in option pricing jump diffusion models. In order to consider the unknown behaviour of the solution in the unbounded part of the spatial domain, a double discretization is proposed. Stability, consistency, and positivity of the resulting explicit scheme are analyzed. Advantages of the method are illustrated with several examples.

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