Abstract
This paper presents a high order multiplication perturbation method for singularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary differential equations (ODEs) are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.
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Project supported by the National Natural Science Foundation of China (Key Program) (Nos. 11132004 and 51078145)
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Zhang, Wz., Huang, Py. High order multiplication perturbation method for singular perturbation problems. Appl. Math. Mech.-Engl. Ed. 34, 1383–1392 (2013). https://doi.org/10.1007/s10483-013-1753-x
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DOI: https://doi.org/10.1007/s10483-013-1753-x
Key words
- singular perturbation problem (SPP)
- high order multiplication perturbation method
- two-point boundary value problem
- boundary layer