Sentence examples for linear collocation method from inspiring English sources
The linear collocation method was used in the BEM calculations (Mosher et al. 1999).
In this paper, we aim to give some algorithms for handling both of linear and nonlinear second-order boundary value problems based on introducing a new operational matrix of derivatives, and then applying Petrov Galerkin method on linear equations and collocation method on nonlinear equations.
In fact, in the literature only one paper by Ma et al. [12] analyzes the convergence order of moving collocation method for linear second-order PDEs - a very simple PDE; however, it is not possible to prove the convergence rates for nonlinear KdV equations.
Muhammad et al. [18] presented a technique for linear integral equations using the Sinc collocation method based on the DE transformation.
In this section, we will use Laguerre wavelets operational matrix of integration combining collocation method to solve linear or nonlinear singular boundary value problems.
Hadizadeh and Asgary [11] using the bivariate Chebyshev collocation method solved the linear Volterra–Fredholm integral equations of the second kind.
The differential equations are transformed by the collocation method to non-linear algebraic equations.
The artificial viscosity has been introduced to capture the exponential features of the exact solution on a uniform mesh and then the B-spline collocation method leads to a tridiagonal linear system.
The governing continuum equations that comprised the balance laws of mass, linear momentum, and energy were modified to include the Hartmann and Hall effects of magnetohydrodynamics, and variable viscosity of the fluid was solved numerically using the successive linearization method together with the Chebyshev collocation method.
The linear equations are then solved using the Chebyshev spectral collocation method [21, 22].
We use the artificial viscosity to capture the exponential features of the exact solution on a uniform mesh and use B-spline collocation method which leads to a tridiagonal linear system.
