A collocation approach for the numerical solution of certain linear retarded and advanced integrodifferential equations with linear functional arguments

2011 ◽  
Vol 27 (2) ◽  
pp. 447-459 ◽  
Author(s):  
Mustafa Gülsu ◽  
Mehmet Sezer
Keyword(s):  
Numerical Solution ◽  
Linear Functional ◽  
Integrodifferential Equations ◽  
Collocation Approach

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.

NUMERICAL SOLUTION FOR THE NONLINEAR EMDEN–FOWLER TYPE EQUATIONS BY A FOURTH-ORDER ADAPTIVE METHOD

2013 ◽  
Vol 11 (01) ◽  
pp. 1350052 ◽  
Author(s):  
S. A. KHURI ◽  
A. SAYFY
Keyword(s):  
Finite Element ◽  
Numerical Solution ◽  
Rate Of Convergence ◽  
Fourth Order ◽  
Numerical Solutions ◽  
Adaptive Method ◽  
B Splines ◽  
Special Cases ◽  
Collocation Approach

A finite element collocation approach, based on cubic B-splines, is manipulated for obtaining numerical solutions of a generalized form of the Emden–Fowler type equations. The rate of convergence is discussed theoretically and verified numerically to be of fourth-order by using the double-mesh principle. The efficiency of the scheme is tested on a number of examples which represent special cases of the problem under consideration. The results are compared with analytical and other numerical solutions that are available in the literature. The proposed method reveals that the outcomes are reliable and very accurate when contrasted with other existing methods.

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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