TY - CONF
T1 - The method of nonlocal transformations: Applications to singularly perturbed boundary-value problems
AU - Polyanin, Andrei D.
AU - Shingareva, Inna K.
PY - 2019/5/7
Y1 - 2019/5/7
N2 - © 2019 Published under licence by IOP Publishing Ltd. We present a method of numerical integration of singularly perturbed boundary-value problems with a small parameter, based on introducing a new nonlocal independent variable. As a result, we obtain more suitable problems that allow the application of standard fixed-step numerical methods. Two test boundary-value problems for second-order ODEs that have monotonic and non-monotonic exact or asymptotic solutions, expressed in elementary functions, are considered. Comparison of numerical, exact, and asymptotic solutions showed the high efficiency of the method based on generalized nonlocal transformations for solving singular boundary-value problems with a small parameter.
AB - © 2019 Published under licence by IOP Publishing Ltd. We present a method of numerical integration of singularly perturbed boundary-value problems with a small parameter, based on introducing a new nonlocal independent variable. As a result, we obtain more suitable problems that allow the application of standard fixed-step numerical methods. Two test boundary-value problems for second-order ODEs that have monotonic and non-monotonic exact or asymptotic solutions, expressed in elementary functions, are considered. Comparison of numerical, exact, and asymptotic solutions showed the high efficiency of the method based on generalized nonlocal transformations for solving singular boundary-value problems with a small parameter.
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U2 - 10.1088/1742-6596/1205/1/012047
DO - 10.1088/1742-6596/1205/1/012047
M3 - Paper
T2 - Journal of Physics: Conference Series
Y2 - 7 May 2019
ER -