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On orthogonal splines and their application in variational-grid methods for solving boundary value problems
| Title | On orthogonal splines and their application in variational-grid methods for solving boundary value problems |
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| Authors | V. L. Leontiev1 1Moscow Institute of Physics and Technology |
| Annotation | The theory of orthogonal splines and its application in mixed variational-grid methods for solving boundary value problems of deformable solid mechanics based on the Reissner variational principle are described. The orthogonalization of Schoenberg cubic spline is considered using the authors geometric procedure, which does not change the finite supports of the splines, unlike the Gram-Schmidt orthogonalization procedure. The results of orthogonalization of Schoenberg splines of the third degree using of auxiliary Schoenberg splines are discussed. Estimates of the approximation error of any function of three Sobolev spaces by orthogonal Schoenberg splines are obtained. The use of orthogonal cubic Schoenberg splines in solving boundary value problems related to systems of partial differential equations is proposed. |
| Keywords | orthogonal splines, the authors geometric procedure for orthogonalizing splines, cubic Schoenberg splines, boundary value problems, mixed variational-grid methods, partial differential equations, approximation error. |
| Citation | Leontiev V. L. ''On orthogonal splines and their application in variational-grid methods for solving boundary value problems'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 150-153. Available at: https://conf.svmo.ru/files/2025/papers/paper30.pdf. - Date of access: 30.08.2025. |
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