The number of meetings in free Poisson traffic

1974 ◽  
Vol 11 (2) ◽  
pp. 320-331
Author(s):  
Hans D. Unkelbach ◽  
Helmut Wegmann
Keyword(s):  
Differential Equation ◽  
Generating Function ◽  
Practical Interest ◽  
Time Interval ◽  
Integro Differential Equation

Using Rényi's model of free Poisson traffic the distribution of the number of meetings of vehicles on a highway section during a given time interval is investigated. An integro-differential equation for the generating function of that variable is deduced and the first moments are calculated. The generating function is given explicitly in simple cases and approximately in cases of practical interest.

The number of meetings in free Poisson traffic

1974 ◽  
Vol 11 (02) ◽  
pp. 320-331
Author(s):  
Hans D. Unkelbach ◽  
Helmut Wegmann
Keyword(s):  
Differential Equation ◽  
Generating Function ◽  
Practical Interest ◽  
Time Interval ◽  
Integro Differential Equation

Using Rényi's model of free Poisson traffic the distribution of the number of meetings of vehicles on a highway section during a given time interval is investigated. An integro-differential equation for the generating function of that variable is deduced and the first moments are calculated. The generating function is given explicitly in simple cases and approximately in cases of practical interest.

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.   

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

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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