We present a family of high-order multi-point finite difference methods for solving nonlinear two-point boundary value problems. The family involves some known methods as specific instances. We also introduce a highly efficient quintic B-spline method for solving nonlinear two-point boundary value problems, which yields an approximate solution in the form of a B-spline representation. This method successfully approximates the solutions to the one-dimensional Bratu, Troesch, and Lane–Emden problems without requirements of any information about the exact solutions.
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International Mathematical Schools 7. Mathematical Schools in Mongolia. In Honor of Academician T. Zhanlav
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Zhanlav, T., Batgerel, B., Otgondorj, K. et al. Higher-Order Finite-Difference Schemes for Nonlinear Two-Point Boundary Value Problems. J Math Sci 279, 850–865 (2024). https://doi.org/10.1007/s10958-024-07065-5
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DOI: https://doi.org/10.1007/s10958-024-07065-5