Merna Aziz - Academia.edu (original) (raw)

Merna Aziz

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Papers by Merna Aziz

Research paper thumbnail of Solving (2+1) Riemann Wave Equation via First Integral Method

MINAR International journal of applied sciences and technology, Dec 1, 2023

This research sought to find an approximate solution to the partial differential equations (PDEs)... more This research sought to find an approximate solution to the partial differential equations (PDEs) by relying on a method based on the commutative algebra theory, and this method is (the first integral method FIM). At first, the order of the partial differential equation was reduced to an ordinary differential equation through traveling wave transformations, then it was solved using the first soft steps of integration, as it produced the approximate solutions to the problem. This method is characterized by being brief, direct and effective when finding the approximate solution to PDEs.

Research paper thumbnail of On the Use of Elzaki Decomposition Method for Solving Higher-Order Integro-Differential Equations

International Journal of Mathematics and Mathematical Sciences

In this article, we implemented the Elzaki decomposition technique (EDM) to solve Volterra–Fredho... more In this article, we implemented the Elzaki decomposition technique (EDM) to solve Volterra–Fredholm integro-differential equations of higher-order. Illustrations are used to test the technique’s accuracy and validity. Comparison among the acquired consequences by EDM and actual solutions have proven the power and accuracy of this technique. This technique is dependable and able to supply analytic remedies for solving such equations.

Research paper thumbnail of Solution of Eighth Order Boundary Value Problems Using Differential Transformation Technique

AL-Rafidain Journal of Computer Sciences and Mathematics

In this paper we have applied the Differential Transform Method (DTM) for solving eighth-order bo... more In this paper we have applied the Differential Transform Method (DTM) for solving eighth-order boundary value problems. The analytical and numerical results of the equations have been obtained in terms of convergent series with the easily computable components. Three examples are considered for the numerical illustrate and implementation of this method. Numerical Comparisons with respect to the analytical solutions have been considered. It is observed that the method is an alternative and efficient for finding the approximate solutions of the boundary values problems.

Research paper thumbnail of The existence and approximation of the periodic solutions for system of first order nonlinear differential equationsby using Lebesgue integrable

JOURNAL OF EDUCATION AND SCIENCE

Research paper thumbnail of The existence and approximation of the periodic solutions for system of second order nonlinear differential equationsby using Lebesgue integrable

JOURNAL OF EDUCATION AND SCIENCE

Research paper thumbnail of Solving (2+1) Riemann Wave Equation via First Integral Method

MINAR International journal of applied sciences and technology, Dec 1, 2023

This research sought to find an approximate solution to the partial differential equations (PDEs)... more This research sought to find an approximate solution to the partial differential equations (PDEs) by relying on a method based on the commutative algebra theory, and this method is (the first integral method FIM). At first, the order of the partial differential equation was reduced to an ordinary differential equation through traveling wave transformations, then it was solved using the first soft steps of integration, as it produced the approximate solutions to the problem. This method is characterized by being brief, direct and effective when finding the approximate solution to PDEs.

Research paper thumbnail of On the Use of Elzaki Decomposition Method for Solving Higher-Order Integro-Differential Equations

International Journal of Mathematics and Mathematical Sciences

In this article, we implemented the Elzaki decomposition technique (EDM) to solve Volterra–Fredho... more In this article, we implemented the Elzaki decomposition technique (EDM) to solve Volterra–Fredholm integro-differential equations of higher-order. Illustrations are used to test the technique’s accuracy and validity. Comparison among the acquired consequences by EDM and actual solutions have proven the power and accuracy of this technique. This technique is dependable and able to supply analytic remedies for solving such equations.

Research paper thumbnail of Solution of Eighth Order Boundary Value Problems Using Differential Transformation Technique

AL-Rafidain Journal of Computer Sciences and Mathematics

In this paper we have applied the Differential Transform Method (DTM) for solving eighth-order bo... more In this paper we have applied the Differential Transform Method (DTM) for solving eighth-order boundary value problems. The analytical and numerical results of the equations have been obtained in terms of convergent series with the easily computable components. Three examples are considered for the numerical illustrate and implementation of this method. Numerical Comparisons with respect to the analytical solutions have been considered. It is observed that the method is an alternative and efficient for finding the approximate solutions of the boundary values problems.

Research paper thumbnail of The existence and approximation of the periodic solutions for system of first order nonlinear differential equationsby using Lebesgue integrable

JOURNAL OF EDUCATION AND SCIENCE

Research paper thumbnail of The existence and approximation of the periodic solutions for system of second order nonlinear differential equationsby using Lebesgue integrable

JOURNAL OF EDUCATION AND SCIENCE

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