Mohammed Al-Refai

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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)
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)
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)