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A new geoid for Brunei Darussalam by the collocation method

100%
Lyszkowicz A., Biryło M., Becek K.
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2014
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vol. 63
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issue 2
2
Content available remote

Numerical solution of fractional differential equations by using fractional B-spline

100%
Jafari H., Khalique C., Ramezani M., Tajadodi H.
Open Physics
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2013
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vol. 11
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issue 10
1372-1376
EN
In this paper, we present fractional B-spline collocation method for the numerical solution of fractional differential equations. We consider this method for solving linear fractional differential equations which involve Caputo-type fractional derivatives. The numerical results demonstrate that the method is efficient and quite accurate and it requires relatively less computational work. For this reason one can conclude that this method has advantage on other methods and hence demonstrates the importance of this work.
3
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A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

88%
Doha E., Bhrawy A., Abdelkawy M.
Open Physics
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2014
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vol. 12
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issue 9
637-653
EN
In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach
4
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Legendre multiwavelet collocation method for solving the linear fractional time delay systems

88%
Yousefi S., Lotfi A.
Open Physics
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2013
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vol. 11
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issue 10
1463-1469
EN
In this article the Legendre multiwavelet basis with aid of collocation method has been applied to give approximate solution for fractional delay systems. The properties of Legendre multiwavelet are presented. These properties together with the collocation method are then utilized to reduce the problem to the solution of algebraic system. Numerical results and comparison with exact solutions in the cases when we have exact solution are given in test examples in order to demonstrate the applicability and efficiency of the method.
5
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Numerical solutions of the reaction diffusion system by using exponential cubic B-spline collocation algorithms

88%
Ersoy O., Dag I.
Open Physics
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2015
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vol. 13
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issue 1
EN
The solutions of the reaction-diffusion system are given by method of collocation based on the exponential B-splines. Thus the reaction-diffusion systemturns into an iterative banded algebraic matrix equation. Solution of the matrix equation is carried out byway of Thomas algorithm. The present methods test on both linear and nonlinear problems. The results are documented to compare with some earlier studies by use of L∞ and relative error norm for problems respectively.
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