Hybrid Spline Difference Method for Steady-State Heat Conduction

Abstract

This work proposes a simple and high-precision hybrid spline difference method, and finds that the computing method of spline difference is as simple as that of the finite-difference method. It also discusses steady-state heat conduction problems to overcome the complex computation and time-consuming problems of the previous spline method. In addition, due to the concept of hybrid parameters, the truncation error of numerical solutions is enhanced to o(h⁴). This method is expected to be a simple and high-precision numerical method that can replace the finite-difference method.

Acknowledgments

Thanks for the subsidy of the Outlay NSC 99-2221-E-035-103- given by the National Science Council, the Republic of China, to help us finish this special research successfully.

Notes

^a A recursive equation unable to be directly expressed as neighboring values.

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