New versions of the least-squares collocation method for solving differential and integral equations
Vasily Shapeev,Sergey Golushko,Vasily Belyaev,Luka Bryndin,Pavel Kirillov +4 more
- Vol. 1715, Iss: 1, pp 012031
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In this paper, the least square collocation method has been used to solve nonlinear systems of partial differential equations, such as the stationary Navier-Stokes equations and integral equations.Abstract:
This paper describes new versions of the least-squares collocation method for solving differential and integral equations. A p-version of the method has been proposed and implemented to solve nonlinear systems of partial differential equations. The stationary Navier-Stokes equations are used as an example. A hp-version of the method has been implemented for the numerical solution of the Fredholm integral equations of the second kind in the one-and two-dimensional cases. This paper shows that approximate solutions obtained by various versions of the least-squares collocation method converge with a high order and agree with analytical solutions of test problems with a high degree of accuracy.read more
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References
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Book
Numerical Methods for Large Eigenvalue Problems
TL;DR: This chapter discusses matrix theory and linear algebra techniques used in spectral approximation, including Krylov subspace methods, and some of the origins of matrix eigenvalue problems.
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A subdomain boundary element method for high‐Reynolds laminar flow using stream function‐vorticity formulation
Matjaž Ramšak,Leopold Škerget +1 more
TL;DR: The paper presents a new formulation of the integral boundary element method (BEM) using subdomain technique and a continuous approximation of the function and the function derivative in the direction normal to the boundary element (further ‘normal flux') is introduced for solving the general form of a parabolic diffusion‐convective equation.
Journal ArticleDOI
A computational method for solving two-dimensional linear fredholm integral equations of the second kind
A. Tari,Sedaghat Shahmorad +1 more
TL;DR: In this paper, an expansion method based on Legendre or any orthogonal polynomials is developed to find numerical solutions of two-dimensional linear Fredholm integral equations, and the error of the method is estimated.
Journal ArticleDOI
High-accuracy versions of the collocations and least squares method for the numerical solution of the Navier-Stokes equations
V. I. Isaev,V. P. Shapeev +1 more
TL;DR: In this article, an approach for the creation of high-accuracy versions of the collocations and least squares method for the numerical solution of the Navier-Stokes equations is proposed.
Journal ArticleDOI
Numerical solution of the linear two-dimensional Fredholm integral equations of the second kind via two-dimensional triangular orthogonal functions
Farshid Mirzaee,Sima Piroozfar +1 more
TL;DR: In this paper, the authors developed two-dimensional triangular orthogonal functions (2D-TFs) for numerical solution of the linear 2D Fredholm integral equations of the second kind.
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