A survey of numerical techniques for solving singularly perturbed ordinary differential equations
Applied Mathematics and Computation
Applied Mathematics and Computation
Journal of Computational and Applied Mathematics
B-spline collocation method for the singular-perturbation problem using artificial viscosity
Computers & Mathematics with Applications
A computational method for self-adjoint singular perturbation problems using quintic spline
Computers & Mathematics with Applications
Computers & Mathematics with Applications
B-splines with artificial viscosity for solving singularly perturbed boundary value problems
Mathematical and Computer Modelling: An International Journal
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In this paper, we propose a B-spline collocation method using artificial viscosity for solving singularly perturbed two-point boundary-value problems (BVPs). The artificial viscosity has been introduced to capture the exponential features of the exact solution on a uniform mesh and the scheme comprises a B-spline collocation method, which leads to a tri-diagonal linear system. The design of artificial viscosity parameter is confirmed to be a crucial ingredient for simulating the solution of the problem. A relevant numerical example is also illustrated to demonstrate the accuracy of the method and to verify computationally the theoretical aspects. The result shows that the B-spline method is feasible and efficient and is found to be in good agreement with the exact solution.