scholarly journals New Iterative Method Based on Laplace Decomposition Algorithm

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Sabir Widatalla ◽  
M. Z. Liu
Keyword(s):  
Iterative Method ◽  
Higher Order ◽  
Decomposition Algorithm ◽  
Computational Time ◽  
Adomian Polynomials ◽  
Different Types ◽  
New Form ◽  
New Iterative Method

We introduce a new form of Laplace decomposition algorithm (LDA). By this form a new iterative method was achieved in which there is no need to calculate Adomian polynomials, which require so much computational time for higher-order approximations. We have implemented this method for the solutions of different types of nonlinear pantograph equations to support the proposed analysis.

scholarly journals New Iterative Methods for Solving Fokker-Planck Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
A. A. Hemeda ◽  
E. E. Eladdad
Keyword(s):  
Iterative Method ◽  
Lagrange Multipliers ◽  
Planck Equation ◽  
Adomian Polynomials ◽  
Adomian Decomposition ◽  
Iteration Methods ◽  
Linear And Nonlinear ◽  
Fokker Planck Equations ◽  
New Iterative Method ◽  
Fokker Planck

In this article, we propose the new iterative method and introduce the integral iterative method to solve linear and nonlinear Fokker-Planck equations and some similar equations. The results obtained by the two methods are compared with those obtained by both Adomian decomposition and variational iteration methods. Comparison shows that the two methods are more effective and convenient to use and overcome the difficulties arising in calculating Adomian polynomials and Lagrange multipliers, which means that the considered methods can simply and successfully be applied to a large class of problems.

An efficient iterative algorithm for the natural convection equations based on finite element method

2018 ◽  
Vol 28 (3) ◽  
pp. 584-605 ◽  
Author(s):  
Lei Wang ◽  
Jian Li ◽  
Pengzhan Huang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Convection ◽  
Iterative Method ◽  
Error Correction ◽  
Computational Time ◽  
Content Type ◽  
Natural Convection Problem ◽  
New Iterative Method ◽  
Element Method

Purpose This paper aims to propose a new highly efficient iterative method based on classical Oseen iteration for the natural convection equations. Design/methodology/approach First, the authors solve the problem by the Oseen iterative scheme based on finite element method, then use the error correction strategy to control the error arising. Findings The new iterative method not only retains the advantage of the Oseen scheme but also saves computational time and iterative step for solving the considered problem. Originality/value In this work, the authors introduce a new iterative method to solve the natural convection equations. The new algorithm consists of the Oseen scheme and the error correction which can control the errors from the iterative step arising for solving the nonlinear problem. Comparing with the classical iterative method, the new scheme requires less iterations and is also capable of solving the natural convection problem at higher Rayleigh number.

scholarly journals Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1665
Author(s):  
Fátima Cruz ◽  
Ricardo Almeida ◽  
Natália Martins
Keyword(s):  
Time Delay ◽  
Fractional Derivatives ◽  
Variational Problems ◽  
Higher Order ◽  
Sufficient Optimality Conditions ◽  
Fractional Operator ◽  
Different Types ◽  
Generalized Fractional Derivatives ◽  
Necessary And Sufficient ◽  
Distributed Order

In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with respect to another function. The main results of this paper are necessary and sufficient optimality conditions for different types of variational problems. Since we are dealing with generalized fractional derivatives, from this work, some well-known results can be obtained as particular cases.

scholarly journals Levels of detail analysis of microwave scattering from human head models for brain stroke detection

PeerJ ◽  
2017 ◽  
Vol 5 ◽  
pp. e4061 ◽  
Author(s):  
Awais Munawar Qureshi ◽  
Zartasha Mustansar
Keyword(s):  
Scattering Problem ◽  
Human Head ◽  
Computational Time ◽  
Head Model ◽  
Microwave Scattering ◽  
Levels Of Detail ◽  
Realistic Head Model ◽  
Different Types ◽  
Brain Stroke ◽  
Brain Tissues

In this paper, we have presented a microwave scattering analysis from multiple human head models. This study incorporates different levels of detail in the human head models and its effect on microwave scattering phenomenon. Two levels of detail are taken into account; (i) Simplified ellipse shaped head model (ii) Anatomically realistic head model, implemented using 2-D geometry. In addition, heterogenic and frequency-dispersive behavior of the brain tissues has also been incorporated in our head models. It is identified during this study that the microwave scattering phenomenon changes significantly once the complexity of head model is increased by incorporating more details using magnetic resonance imaging database. It is also found out that the microwave scattering results match in both types of head model (i.e., geometrically simple and anatomically realistic), once the measurements are made in the structurally simplified regions. However, the results diverge considerably in the complex areas of brain due to the arbitrary shape interface of tissue layers in the anatomically realistic head model.After incorporating various levels of detail, the solution of subject microwave scattering problem and the measurement of transmitted and backscattered signals were obtained using finite element method. Mesh convergence analysis was also performed to achieve error free results with a minimum number of mesh elements and a lesser degree of freedom in the fast computational time. The results were promising and the E-Field values converged for both simple and complex geometrical models. However, the E-Field difference between both types of head model at the same reference point differentiated a lot in terms of magnitude. At complex location, a high difference value of 0.04236 V/m was measured compared to the simple location, where it turned out to be 0.00197 V/m. This study also contributes to provide a comparison analysis between the direct and iterative solvers so as to find out the solution of subject microwave scattering problem in a minimum computational time along with memory resources requirement.It is seen from this study that the microwave imaging may effectively be utilized for the detection, localization and differentiation of different types of brain stroke. The simulation results verified that the microwave imaging can be efficiently exploited to study the significant contrast between electric field values of the normal and abnormal brain tissues for the investigation of brain anomalies. In the end, a specific absorption rate analysis was carried out to compare the ionizing effects of microwave signals to different types of head model using a factor of safety for brain tissues. It is also suggested after careful study of various inversion methods in practice for microwave head imaging, that the contrast source inversion method may be more suitable and computationally efficient for such problems.

scholarly journals Aboodh Transform Iterative Method for Spatial Diffusion of a Biological Population with Fractional-Order

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 155
Author(s):  
Gbenga O. Ojo ◽  
Nazim I. Mahmudov
Keyword(s):  
Iterative Method ◽  
Fractional Order ◽  
Population Model ◽  
Numerical Solutions ◽  
Computational Effort ◽  
Spatial Diffusion ◽  
Transform Method ◽  
Biological Population ◽  
The Laplace Transform ◽  
New Iterative Method

In this paper, a new approximate analytical method is proposed for solving the fractional biological population model, the fractional derivative is described in the Caputo sense. This method is based upon the Aboodh transform method and the new iterative method, the Aboodh transform is a modification of the Laplace transform. Illustrative cases are considered and the comparison between exact solutions and numerical solutions are considered for different values of alpha. Furthermore, the surface plots are provided in order to understand the effect of the fractional order. The advantage of this method is that it is efficient, precise, and easy to implement with less computational effort.

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