Uroosa Arshad
Federal Urdu University of Arts, Sciences and Technolgy, Karachi, Mathematical Sciences, Cooperative Lecturer
Uroosa Arshad is a Cooperative lecturer of Mathematics at Federal Urdu University of Arts, Science & Technology in Karachi, Pakistan. Uroosa Arshad graduated with Master’s Degree from the Federal Urdu University of Arts, Science & Technology in Mathematics. She has now doing M.Phil. leading to Ph.D. from the NED University in Karachi, Pakistan in Mathematics.
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lies in the error analysis between exact solutions and approximate solutions obtained by these two methods which proves that approximate solutions obtained by Alternative Variation Iteration Method converge very rapidly to the exact solutions. Both methods provide
analytical solution in the form of a convergent series with components that are easily computable, requiring no linearization or small perturbation.
of a small parameter assumption as its earlier classical
counterparts do. Some examples have been presented to exhibit how simply and efficiently the proposed method works. After deriving the exact solution of the Riccati equation, the capability and the simplicity of the proposed technique is clarified. A percentage error for each example has also been presented.
related to the Laplace Transform. In the following paper, the Elzaki Transform Algorithm, which has been built
on the Decomposition Method, is presented to be applied to find approximate solution of a class of non-linear, initial value problems. This method gives an approximate solution in a Convergent-Series form with easily computable components necessitating no linearization or a low perturbation criterion. The most important part of this paper is the error analysis conducted between exact solutions and pade approximate solutions; it proves that our approximate solutions narrow in rapidly to the exact solutions. Moreover, as we will discuss after the results
are resented, this algorithm can also be applicable to more general classes of linear and nonlinear differential
equations.
of the Elzaki transform on fractional derivatives. The Elzaki transformation may be used to solve mathematical problems without resorting to a new frequency domain. Once we establish this connection firmly in the general setting, we turn our attention to the application of the Elzaki transform method to some non-homogeneous fractional, ordinary differential equations. Ultimately, we acquire the graphical solution of the problem by using Matlab 2013a, developed by MathWorks
of fractional differential equations.
The Klein-Gordon equation is the name given to the equation of motion of a quantum scalar or pseudo scalar field, a field whose quanta are spin-less particles. It describes the quantum amplitude for finding a point particle in various places, the relativistic wave function, but the particle propagates both forwards and backwards in time. The Perturbation Iteration Transform Method (PITM) is a combined form of the Laplace Transform Method and Perturbation Iteration Algorithm. The method provides the solution in the form of a rapidly convergent series. Some numerical examples are used to illustrate the preciseness and effectiveness of the proposed method. The results show that the PITM
is very efficient, simple and can be applied to other nonlinear problems.
lies in the error analysis between exact solutions and approximate solutions obtained by these two methods which proves that approximate solutions obtained by Alternative Variation Iteration Method converge very rapidly to the exact solutions. Both methods provide
analytical solution in the form of a convergent series with components that are easily computable, requiring no linearization or small perturbation.
of a small parameter assumption as its earlier classical
counterparts do. Some examples have been presented to exhibit how simply and efficiently the proposed method works. After deriving the exact solution of the Riccati equation, the capability and the simplicity of the proposed technique is clarified. A percentage error for each example has also been presented.
related to the Laplace Transform. In the following paper, the Elzaki Transform Algorithm, which has been built
on the Decomposition Method, is presented to be applied to find approximate solution of a class of non-linear, initial value problems. This method gives an approximate solution in a Convergent-Series form with easily computable components necessitating no linearization or a low perturbation criterion. The most important part of this paper is the error analysis conducted between exact solutions and pade approximate solutions; it proves that our approximate solutions narrow in rapidly to the exact solutions. Moreover, as we will discuss after the results
are resented, this algorithm can also be applicable to more general classes of linear and nonlinear differential
equations.
of the Elzaki transform on fractional derivatives. The Elzaki transformation may be used to solve mathematical problems without resorting to a new frequency domain. Once we establish this connection firmly in the general setting, we turn our attention to the application of the Elzaki transform method to some non-homogeneous fractional, ordinary differential equations. Ultimately, we acquire the graphical solution of the problem by using Matlab 2013a, developed by MathWorks
of fractional differential equations.
The Klein-Gordon equation is the name given to the equation of motion of a quantum scalar or pseudo scalar field, a field whose quanta are spin-less particles. It describes the quantum amplitude for finding a point particle in various places, the relativistic wave function, but the particle propagates both forwards and backwards in time. The Perturbation Iteration Transform Method (PITM) is a combined form of the Laplace Transform Method and Perturbation Iteration Algorithm. The method provides the solution in the form of a rapidly convergent series. Some numerical examples are used to illustrate the preciseness and effectiveness of the proposed method. The results show that the PITM
is very efficient, simple and can be applied to other nonlinear problems.