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The Telescoping Decomposition Method (TDM) is a new iterative method to obtain numerical and analytical solutions for first order nonlinear differential equations. The method is a modified form of the well-known Adomian Decomposition Method (ADM) where the Adomian polynomials have not to be calculating. The (TDM) is easier to apply and offers better… (More)

We correct a recent result concerning the fractional derivative at extreme points. We then establish new results for the Caputo and Riemann-Liouville fractional derivatives at extreme points.

- Kamel Al-khaled, Mohammed Al-Refai, Ameen Alawneh
- Applied Mathematics and Computation
- 2008

A non-local elliptic equation, for which comparison methods are applicable, associated with Robin boundary conditions is considered. Upper and lower solutions for this problem are obtained by solving algebraic equations. These upper and lower solutions are used to obtain analytical bounds for the critical (blow-up) parameter of the problem. Numerical… (More)

Modern software systems that play critical roles in society's infrastructures are often required to change at runtime so that they can continuously provide essential services in the dynamic environments they operate in. Updating open, distributed software systems at runtime is very challenging. Using runtime models as an interface for updating software at… (More)

- Mohammed Al-Refai, Sudipto Ghosh, Walter Cazzola
- 2016 IEEE International Conference on Software…
- 2016

An increasing number of modern software systems need to be adapted at runtime without stopping their execution. Runtime adaptations can introduce faults in existing functionality, and thus, regression testing must be conducted after an adaptation is performed but before the adaptation is deployed to the running system. Regression testing must be completed… (More)

In this paper, we suggest a jump diffusion model in markets during financial crisis. Using risk-neutral pricing, we derive a partial differential equation (P.D.E.) for the prices of European options. We find a closed form solution of the P.D.E. in the particular case where the stock price is too large. Then, we use such a solution as a boundary condition in… (More)

- Mohammed Al-Refai, Nikos I. Kavallaris
- Computers & Mathematics with Applications
- 2013