Approximate method for the numerical solution of singular perturbation problems |
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| Affiliation: | 1. Universidad Autónoma de Baja California, Facultad de Ciencias de la Ingeniería, Administrativas y Sociales, Tecate, C.P. 21460, Baja California, Mexico;2. Universidad Nacional Autónoma de México, Instituto de Ingeniería, Coyoacán, Ciudad de México, C.P. 04510, Mexico;3. Instituto Politécnico Nacional, Sección de Estudios de Investigación y Posgrado, ESIME-UPT, Ciudad de México, C.P. 07430, Mexico;1. Department of Automation and Systems (DAS), UFSC, PO BOX 476, Florianópolis, SC 88040-900, Brazil;2. Department of Control Engineering and System Analysis (SAAS), ULB, Brussels B-1050, Belgium |
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| Abstract: | We present an approximate method for the numerical solution of linear singularly perturbed two point boundary value problems in ordinary differential equations with a boundary layer on the left end of the underlying interval. It is motivated by the asymptotic behavior of singular perturbation problems. The original problem is divided into inner and outer region problems. The reduced problem is solved to obtain the terminal boundary condition. Then, a new inner region problem is created and solved as a two point boundary value problem. In turn, the outer region problem is also modified and the resulting problem is efficiently treated by employing the trapezoidal formula coupled with discrete invariant imbedding algorithm. The proposed method is iterative on the terminal point. Some numerical experiments have been included to demonstrate its applicability. |
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