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BSU Bulletin. Mathematics, Informatics

Bibliographic description:
Abiduev P. L.
,
Darmaev T. G.
,
Liseikin V. D.
NUMERICAL SOLUTION OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS OF THE 4TH ORDER // BSU Bulletin. Mathematics, Informatics. - 2022. №4. . - С. 3-11.
Title:
NUMERICAL SOLUTION OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS OF THE 4TH ORDER
Financing:
Codes:
DOI: 10.18101/2304-5728-2022-4-3-11UDK: 519.62
Annotation:
This paper deals with a 4th-order differential equation with a small pa- rameter at the higher derivative. A solution algorithm is proposed based on the applica- tion of a special non-uniform difference grid, with the differential equation operator approximated in two ways: 1) the 4th order operator is replaced by a more convenient operator, which is split into two operators, i.e. instead of one equation, a system of two equations of the second order is considered; 2) by the method of integral identities, the operator is approximated on a five-point pattern. In the first approach, theorems on uniform convergence on the non-uniform difference grid proposed in the work have been proved. In the second approach, the order of uniform convergence was shown by numerical experiment. The solution of the system of difference equations was carried out by a non-monotonic run. The described numerical algorithm was used to solve the linearized problem of longitudinal-transverse bending of an elastic beam with embed- ded ends under the action of a distributed load.
Keywords:
numerical solution, singularly perturbed boundary value problem of the 4th order, uniform convergence, method of integral identities, non-uniform difference grid.
List of references: