Variational principle for some nonlinear problems. (English) Zbl 07489147
Summary: A variational principle is established by the semi-inverse method and used to solve approximately a nonlinear problem by the Ritz method. In this process, it may be difficult to solve a large system of algebraic equations, the Groebner bases theory (Buchberger’s algorithm) is applied to solve this problem. The results show that the variational approach is much simpler and more efficient.
MSC:
| 65-XX | Numerical analysis |
| 35A15 | Variational methods applied to PDEs |
| 35M12 | Boundary value problems for PDEs of mixed type |
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