Dr. W. Wahied - Academia.edu (original) (raw)
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Papers by Dr. W. Wahied
Global Journal of Science Frontier Research, 2015
In this paper, we consider a non-local mixed integral equation in position and time in the space ... more In this paper, we consider a non-local mixed integral equation in position and time in the space 2 L 1,1 C 0,T ;T. Then, using a quadratic numerical method, we have a system of Fredholm integral equations (SFIEs), where the existence of a unique solution is considered. Moreover, we consider Product Nystrom method (PNM), as a famous method to solve the singular integral equations, to obtain an algebraic system. Finally, some numerical results are considered, and the error estimate, in each case, is computed.
In this paper, we consider the nonlocal FredholmVolterra integral equation of the second kind, wi... more In this paper, we consider the nonlocal FredholmVolterra integral equation of the second kind, with continuous kernels. We consider three different numerical methods,the Trapezoidal rule, Simpson rule and Collocation method to reduce the nonlocal F-VIE to a nonlocal algebraic system of equations. The algebraic system is computed numerically, when the historical memory of the problem (nonlocal function) takes three cases: when there is no memory, when the memory is linear and when the memory is nonlinear. Moreover, the estimate error, in each method and each case, is computed. Here, we deduce that, the error in the absence of memory is larger than in the linear memory. Moreover, the error of the linear memory is larger than the nonlinear memory. Keyword: nonlocal Fredholm-Volterra integral equation (nonlocal F-VIE), numerical methods, algebraic system (AS), the error estimate. MSC (2010): 45B05, 45G10, 60R.
Global Journal of Science Frontier Research, 2015
In this paper, we consider a non-local mixed integral equation in position and time in the space ... more In this paper, we consider a non-local mixed integral equation in position and time in the space 2 L 1,1 C 0,T ;T. Then, using a quadratic numerical method, we have a system of Fredholm integral equations (SFIEs), where the existence of a unique solution is considered. Moreover, we consider Product Nystrom method (PNM), as a famous method to solve the singular integral equations, to obtain an algebraic system. Finally, some numerical results are considered, and the error estimate, in each case, is computed.
In this paper, we consider the nonlocal FredholmVolterra integral equation of the second kind, wi... more In this paper, we consider the nonlocal FredholmVolterra integral equation of the second kind, with continuous kernels. We consider three different numerical methods,the Trapezoidal rule, Simpson rule and Collocation method to reduce the nonlocal F-VIE to a nonlocal algebraic system of equations. The algebraic system is computed numerically, when the historical memory of the problem (nonlocal function) takes three cases: when there is no memory, when the memory is linear and when the memory is nonlinear. Moreover, the estimate error, in each method and each case, is computed. Here, we deduce that, the error in the absence of memory is larger than in the linear memory. Moreover, the error of the linear memory is larger than the nonlinear memory. Keyword: nonlocal Fredholm-Volterra integral equation (nonlocal F-VIE), numerical methods, algebraic system (AS), the error estimate. MSC (2010): 45B05, 45G10, 60R.