scholarly journals Schauder estimates for an integro-differential equation with applications to a nonlocal Burgers equation

2018 ◽  
Vol 27 (4) ◽  
pp. 667-677 ◽  
Author(s):  
Cyril Imbert ◽  
Tianling Jin ◽  
Roman Shvydkoy
Keyword(s):  
Differential Equation ◽  
Burgers Equation ◽  
Schauder Estimates ◽  
Integro Differential Equation

scholarly journals Interior Schauder Estimates for Elliptic Equations Associated with Lévy Operators

2021 ◽  
Author(s):  
Franziska Kühn
Keyword(s):  
Differential Equation ◽  
Wide Class ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Infinitesimal Generator ◽  
Transition Density ◽  
Regularity Of Solutions ◽  
Local Regularity ◽  
Schauder Estimates ◽  
Integro Differential Equation

AbstractWe study the local regularity of solutions f to the integro-differential equation $$ Af=g \quad \text{in } U $$ A f = g in U for open sets $U \subseteq \mathbb {R}^{d}$ U ⊆ ℝ d , where A is the infinitesimal generator of a Lévy process (Xt)t≥ 0. Under the assumption that the transition density of (Xt)t≥ 0 satisfies a certain gradient estimate, we establish interior Schauder estimates for both pointwise and weak solutions f. Our results apply for a wide class of Lévy generators, including generators of stable Lévy processes and subordinated Brownian motions.

Some numerical graphs with successive approximation method of fractional integro–differential equation

2019 ◽  
Vol 8 (4) ◽  
pp. 36
Author(s):  
Samir H. Abbas
Keyword(s):  
Differential Equation ◽  
Successive Approximation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Successive Approximation Method ◽  
Integro Differential Equation

This paper studies the existence and uniqueness solution of fractional integro-differential equation, by using some numerical graphs with successive approximation method of fractional integro –differential equation. The results of written new program in Mat-Lab show that the method is very interested and efficient. Also we extend the results of Butris [3].

Normalization Bernstein Basis For Solving Fractional Fredholm-Integro Differential Equation

2018 ◽  
pp. 491
Author(s):  
Abdul Khaleq O. Al-Jubory ◽  
Shaymaa Hussain Salih
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear System ◽  
Differential Equations ◽  
Bernstein Basis ◽  
Traditional Methods ◽  
Integro Differential Equation

In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations  nonhomogeneous  of the second type (LFFIDEs). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDEs) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDEs) by the assistance of Matlab10.   

THE FORWARD PDE FOR EUROPEAN OPTIONS ON STOCKS WITH FIXED FRACTIONAL JUMPS

2005 ◽  
Vol 08 (02) ◽  
pp. 239-253 ◽  
Author(s):  
PETER CARR ◽  
ALIREZA JAVAHERI
Keyword(s):  
Differential Equation ◽  
Closed Form ◽  
Stock Price ◽  
Arrival Rate ◽  
European Options ◽  
Standard Assumption ◽  
Integro Differential Equation ◽  
Local Variance ◽  
Calendar Dates

We derive a partial integro differential equation (PIDE) which relates the price of a calendar spread to the prices of butterfly spreads and the functions describing the evolution of the process. These evolution functions are the forward local variance rate and a new concept called the forward local default arrival rate. We then specialize to the case where the only jump which can occur reduces the underlying stock price by a fixed fraction of its pre-jump value. This is a standard assumption when valuing an option written on a stock which can default. We discuss novel strategies for calibrating to a term and strike structure of European options prices. In particular using a few calendar dates, we derive closed form expressions for both the local variance and the local default arrival rate.

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