scholarly journals New Numerical Method for the Rotation form of the Oseen Problem with Corner Singularity

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 54 ◽  
Author(s):  
Viktor A. Rukavishnikov ◽  
Alexey V. Rukavishnikov
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Velocity Field ◽  
Convergence Rate ◽  
Numerical Approach ◽  
Corner Singularity ◽  
Computational Simulations ◽  
Oseen Problem ◽  
Oseen System ◽  
Solution Velocity

In the paper, a new numerical approach for the rotation form of the Oseen system in a polygon Ω with an internal corner ω greater than 180 ∘ on its boundary is presented. The results of computational simulations have shown that the convergence rate of the approximate solution (velocity field) by weighted FEM to the exact solution does not depend on the value of the internal corner ω and equals O ( h ) in the norm of a space W 2 , ν 1 ( Ω ) .

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

scholarly journals Numerical Approach of Linear Volterra Integro-Differential Equations Using Generalized Spline Functions

2012 ◽  
Vol 9 (4) ◽  
pp. 734-740
Author(s):  
Baghdad Science Journal
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Numerical Approach ◽  
Polynomial Spline ◽  
Spline Functions

This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

Analysis of Deep Beams

1951 ◽  
Vol 18 (2) ◽  
pp. 163-172
Author(s):  
H. D. Conway ◽  
L. Chow ◽  
G. W. Morgan
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Stress Distribution ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Normal Stress ◽  
Stress Function ◽  
Beam Theory ◽  
Deep Beam ◽  
Stress Functions

Abstract This paper presents a method of analyzing the stress distribution in a deep beam of finite length by superimposing two stress functions. The first stress function is chosen in the form of a trigonometric series which satisfies all but one of the boundary conditions—that of zero normal stress on the ends of the beam. The principle of least work is then used to obtain a second stress function giving the distribution of normal stress on the ends which is left by the first stress function. By superimposing the two solutions, all the boundary conditions are satisfied. Two particular cases of a given type of loading are solved in this way to investigate the stresses in a deep beam and their deviation from the ordinary beam theory. In addition, an approximate solution by the numerical method of finite difference is worked out for one of the two cases. Results from the two methods are compared and discussed. A method of obtaining an exact solution to the problem is given in an Appendix.

On a new modified fractional analysis of Nagumo equation

2019 ◽  
Vol 12 (03) ◽  
pp. 1950034 ◽  
Author(s):  
Khaled M. Saad ◽  
Si̇nan Deni̇z ◽  
Dumi̇tru Baleanu
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Fractional Derivatives ◽  
Transform Method ◽  
Average Residual ◽  
Homotopy Analysis ◽  
Fractional Analysis ◽  
Nagumo Equation ◽  
Modified Equation

In this work, a new modified fractional form of the Nagumo equation has been presented and deeply analyzed. Using the Caputo–Fabrizio and Atangana–Baleanu time-fractional derivatives, classical Nagumo model is transformed to a new fractional version. The modified equation has been solved by using the homotopy analysis transform method. The convergence analysis has been also examined with the help of the so-called [Formula: see text]-curves and average residual error. Comparing the obtained approximate solution with the exact solution leaves no doubt believing that the proposed technique is very efficient and converges toward the exact solution very rapidly.

An Algorithm for the Approximate Solution of the Fractional Riccati Differential Equation

2019 ◽  
Vol 20 (6) ◽  
pp. 661-674
Author(s):  
S. S. Ezz-Eldien ◽  
J. A. T. Machado ◽  
Y. Wang ◽  
A. A. Aldraiweesh
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Chebyshev Polynomials ◽  
Unknown Function ◽  
Numerical Approach ◽  
Continuous Functions ◽  
Basis Functions ◽  
Real Constant ◽  
Riccati Differential Equation ◽  
Suggested Approach

AbstractThis manuscript develops a numerical approach for approximating the solution of the fractional Riccati differential equation (FRDE): $$\begin{align*}D^{\mu}&u(x)+a(x) u^2(x)+b(x) u(x)= g(x),\quad 0\leq \mu \leq 1,\quad 0\leq x \leq t,\\&u(0)=d,\end{align*}$$where u(x) is the unknown function, a(x), b(x) and g(x) are known continuous functions defined in [0,t] and d is a real constant. The proposed method is applied for solving the FRDE with shifted Chebyshev polynomials as basis functions. In addition, the convergence analysis of the suggested approach is investigated. The efficiency of the algorithm is demonstrated by means of several examples and the results compared with those given using other numerical schemes.

scholarly journals The Unique Positive Solution for Singular Hadamard Fractional Boundary Value Problems

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Jinxiu Mao ◽  
Zengqin Zhao ◽  
Chenguang Wang
Keyword(s):  
Exact Solution ◽  
Convergence Rate ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Approximation Error ◽  
Iterative Solution ◽  
Unique Positive Solution ◽  
Fractional Boundary Value Problems

In this paper, we investigate singular Hadamard fractional boundary value problems. The existence and uniqueness of the exact iterative solution are established only by using an iterative algorithm. The iterative sequences have been proved to converge uniformly to the exact solution, and estimation of the approximation error and the convergence rate have also been derived.

scholarly journals Reproducing Kernel Method for Solving Nonlinear Fractional Fredholm Integrodifferential Equation

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Bothayna S. H. Kashkari ◽  
Muhammed I. Syam
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Integrodifferential Equation ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Integrodifferential Equations ◽  
Reproducing Kernel Method ◽  
Numerical Studies ◽  
Uniformly Convergence ◽  
Present Algorithm

This article is devoted to both theoretical and numerical studies of nonlinear fractional Fredholm integrodifferential equations. In this paper, we implement the reproducing kernel method (RKM) to approximate the solution of nonlinear fractional Fredholm integrodifferential equations. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the solution of the nonlinear fractional Fredholm integrodifferential equation. Uniformly convergence of the approximate solution produced by the RKM to the exact solution is proven.

scholarly journals Analytic Solution for Systems of Two-Dimensional Time Conformable Fractional PDEs by Using CFRDTM

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Abir Chaouk ◽  
Maher Jneid
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Analytic Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Two Dimensional ◽  
Fractional Pdes ◽  
Differential Transform ◽  
Computational Work ◽  
Similar Solutions

In this study we use the conformable fractional reduced differential transform (CFRDTM) method to compute solutions for systems of nonlinear conformable fractional PDEs. The proposed method yields a numerical approximate solution in the form of an infinite series that converges to a closed form solution, which is in many cases the exact solution. We inspect its efficiency in solving systems of CFPDEs by working on four different nonlinear systems. The results show that CFRDTM gave similar solutions to exact solutions, confirming its proficiency as a competent technique for solving CFPDEs systems. It required very little computational work and hence consumed much less time compared to other numerical methods.

Estimation of Dynamic Forces in Very High-Speed Impact Forging

1966 ◽  
Vol 88 (4) ◽  
pp. 369-372 ◽  
Author(s):  
M. J. Hillier
Keyword(s):  
Approximate Solution ◽  
Velocity Field ◽  
Plane Strain ◽  
Energy Method ◽  
Coulomb Friction ◽  
High Speed ◽  
Admissible Velocity ◽  
High Speed Impact ◽  
Dynamic Forces ◽  
Very High

A study is made of three methods of estimating die loads in impact forging: By approximate solution of the equations of equilibrium; by an energy method, assuming plane sections remain plane; and using the energy method in association with a kinematically admissible velocity field. Results are given for die pressures and die loads for axisymmetric and plane-strain forging of disks and slabs with smooth dies, perfectly rough dies, and for the case of Coulomb friction.

scholarly journals Numerical solution of nonlinear system of integro-differential equations using Chebyshev wavelets

2015 ◽  
Vol 11 (2) ◽  
pp. 15-34
Author(s):  
H. Aminikhah ◽  
S. Hosseini
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Nonlinear System ◽  
Differential Equations ◽  
Numerical Solution ◽  
Chebyshev Wavelets ◽  
Linear And Nonlinear

Abstract This paper introduces an approach for obtaining the numerical solution of the linear and nonlinear integro-differential equations using Chebyshev wavelets approximations. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique and the results have been compared with the exact solution. Comparison of the approximate solution with exact solution shows that the used method is effectiveness and practical for classes of linear and nonlinear system of integro-differential equations.

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