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Numerical analysis of the direct method for 3D Maxwell’s equation in Kerr-type nonlinear media

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Abstract

Recently, a so-called direct method has been developed for solving 2D Maxwell’s equations in Kerr-type nonlinear media. This method is free of iteration error and more efficient than classical iterative method. We investigate this method from a theoretical point of view by proving the stability of 3D Maxwell’s equations. Numerical results have been achieved to verify the second-order convergence rate in both time and space.

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Acknowledgements

We are very grateful to two anonymous referees for their insightful comments on improving the paper.

Funding

This work was supported by the National Natural Science Foundation of China (Nos. 11961036, 12201263), the Natural Science Foundation of Jiangxi Province (No. 20161ACB20006), and Science Fund for Distinguished Young Scholars of Jiangxi Province (No. 20224ACB218001).

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Correspondence to Meng Chen.

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Communicated by Ilaria Perugia.

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Chen, M., Gao, R., He, Y. et al. Numerical analysis of the direct method for 3D Maxwell’s equation in Kerr-type nonlinear media. Adv Comput Math 49, 34 (2023). https://doi.org/10.1007/s10444-023-10029-z

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