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.
|Journal||Journal of Physics: Conference Series|
|Publication status||Published - 4 Jan 2021|
|Event||International Conference on Marchuk Scientific Readings 2020, MSR 2020 - Akademgorodok, Novosibirsk, Russian Federation|
Duration: 19 Oct 2020 → 23 Oct 2020