I want to solve some singularly perturbed boundary value problems. It's clear in the quintic b-spline collocation point, there are four factitious points which will going to eliminate from algebraic differential equations(ADEs) by substituting the boundary conditions. Now, to do this elimination, is that possible to use Dirichlet boundary condition instead of Neumann or mixed BC?
Yes in classical Cubic/Quintic B Spline collocation method, it is easier to deal with Neumann's BC than Dirichlet's BC. From Dirichlet's BC we get derivative condition and use it at the boundary. For more detail, you can see our papers with Geeta Arora. Due to this reasons we have modified Cubic B Spline and Quintic B Spline on the boundary so that Dirichlet's BC can be applied with ease.
Yes in classical Cubic/Quintic B Spline collocation method, it is easier to deal with Neumann's BC than Dirichlet's BC. From Dirichlet's BC we get derivative condition and use it at the boundary. For more detail, you can see our papers with Geeta Arora. Due to this reasons we have modified Cubic B Spline and Quintic B Spline on the boundary so that Dirichlet's BC can be applied with ease.
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