Abstract
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.
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Chang, J., Yang, Q., Zhao, L. (2011). Solving Singular Perturbation Problems by B-Spline and Artificial Viscosity Method. In: Liu, B., Chai, C. (eds) Information Computing and Applications. ICICA 2011. Lecture Notes in Computer Science, vol 7030. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25255-6_94
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DOI: https://doi.org/10.1007/978-3-642-25255-6_94
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25254-9
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