waleed adel
I'm currently an assistant professor in the department of mathematics at Mansoura university. My work focuses on the numerical treatment of differential equations and their analysis of it. My goal is to learn the development of new numerical techniques for solving differential equations both partial and ordinary and its error estimation. Also, I am reviewer for some of the most mathematics prestigious journals and member for the AMS (American mathematical society).
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Papers by waleed adel
nonlinear tenth and twelfth-order boundary-value problems. Properties of Euler polynomials
and some operationalmatrices are first presented. These properties are then used to reduce the
tenth and twelfth-order boundary-value problems into a system of either linear or nonlinear
algebraic equations. Numerical examples illustrate the effectiveness of the method and its
possibility of applications to a wide class of problems. The comparison with other method
are made. It is shown that Euler collocation method gives better results.
Type equations (NWS) are obtained using di�erent cubic B-spline basis. A
linear Von-Neumann stability analysis shows that the numerical scheme is
unconditionally stable. Accuracy of the method is discussed by computing the
max numerical error. The numerical result shows that the presented method
is a successful numerical technique for solving NWS equation.
generalized fifth-order nonlinear evolution equations. Applying Von-Neumann stability analysis, the proposed technique
is shown to be unconditionally stable. The accuracy of the presented method is demonstrated by a test problem. The
numerical results are found to be in good agreement with the exact solution.
Books by waleed adel
branches as in numerical analysis, ordinary and partial differential equations,
integral equations and statistical analysis. It has also many applications in
science, engineering, economics, biology and medicine, etc.
In this book, we study cubic B-spline in calculating numerical
solutions for second order parabolic partial differential equations. In addition,
we use quartic B-spline in calculating numerical solutions for third order
nonlinear partial differential equations. Moreover, sextic B-splines are used
to solve fifth order partial differential equations.
nonlinear tenth and twelfth-order boundary-value problems. Properties of Euler polynomials
and some operationalmatrices are first presented. These properties are then used to reduce the
tenth and twelfth-order boundary-value problems into a system of either linear or nonlinear
algebraic equations. Numerical examples illustrate the effectiveness of the method and its
possibility of applications to a wide class of problems. The comparison with other method
are made. It is shown that Euler collocation method gives better results.
Type equations (NWS) are obtained using di�erent cubic B-spline basis. A
linear Von-Neumann stability analysis shows that the numerical scheme is
unconditionally stable. Accuracy of the method is discussed by computing the
max numerical error. The numerical result shows that the presented method
is a successful numerical technique for solving NWS equation.
generalized fifth-order nonlinear evolution equations. Applying Von-Neumann stability analysis, the proposed technique
is shown to be unconditionally stable. The accuracy of the presented method is demonstrated by a test problem. The
numerical results are found to be in good agreement with the exact solution.
branches as in numerical analysis, ordinary and partial differential equations,
integral equations and statistical analysis. It has also many applications in
science, engineering, economics, biology and medicine, etc.
In this book, we study cubic B-spline in calculating numerical
solutions for second order parabolic partial differential equations. In addition,
we use quartic B-spline in calculating numerical solutions for third order
nonlinear partial differential equations. Moreover, sextic B-splines are used
to solve fifth order partial differential equations.