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Han, J., & Jentzen, A. (2017). Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Communications in mathematics and statistics, 5(4), 349-380.Search in Google Scholar
Kravchenko, V. V., Otero, J. A., & Torba, S. M. (2017). Analytic approximation of solutions of parabolic partial differential equations with variable coefficients. Advances in Mathematical Physics, 2017(1), 2947275.Search in Google Scholar
Das, P. (2018). A higher order difference method for singularly perturbed parabolic partial differential equations. Journal of Difference Equations and Applications, 24(3), 452-477.Search in Google Scholar
Das, A., & Natesan, S. (2018). Second-order uniformly convergent numerical method for singularly perturbed delay parabolic partial differential equations. International Journal of Computer Mathematics, 95(3), 490-510.Search in Google Scholar
Arora, G., & Joshi, V. (2018). A computational approach for solution of one dimensional parabolic partial differential equation with application in biological processes. Ain Shams Engineering Journal, 9(4), 1141-1150.Search in Google Scholar
Garabedian, P. R. (2023). Partial differential equations (Vol. 325). American Mathematical Society.Search in Google Scholar
Nadeem, M., Li, F., & Ahmad, H. (2019). Modified Laplace variational iteration method for solving fourth-order parabolic partial differential equation with variable coefficients. Computers & Mathematics with Applications, 78(6), 2052-2062.Search in Google Scholar
Salama, A. A., & Al-Amery, D. G. (2017). A higher order uniformly convergent method for singularly perturbed delay parabolic partial differential equations. International Journal of Computer Mathematics, 94(12), 2520-2546.Search in Google Scholar
Hutzenthaler, M., Jentzen, A., Kruse, T., Anh Nguyen, T., & von Wurstemberger, P. (2020). Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations. Proceedings of the Royal Society A, 476(2244), 20190630.Search in Google Scholar
Govindarao, L., & Mohapatra, J. (2020). Numerical analysis and simulation of delay parabolic partial differential equation involving a small parameter. Engineering Computations, 37(1), 289-312.Search in Google Scholar
Beck, C., Hutzenthaler, M., & Jentzen, A. (2021). On nonlinear Feynman-Kac formulas for viscosity solutions of semilinear parabolic partial differential equations. Stochastics and Dynamics, 21(08), 2150048.Search in Google Scholar
Zhang, Z., Song, X., Sun, X., & Stojanovic, V. (2023). Hybrid-driven-based fuzzy secure filtering for nonlinear parabolic partial differential equation systems with cyber attacks. International Journal of Adaptive Control and Signal Processing, 37(2), 380-398.Search in Google Scholar
Reinhardt, C., & James, J. M. (2019). Fourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation. Indagationes Mathematicae, 30(1), 39-80.Search in Google Scholar
Bleecker, D. (2018). Basic partial differential equations. Chapman and Hall/CRC.Search in Google Scholar
Abdulla-Al-Mamun, M. S. A., & Miah, M. M. (2018). A study on an analytic solution 1D heat equation of a parabolic partial differential equation and implement in computer programming. International Journal of Scientific & Engineering Research, 9.Search in Google Scholar
Gowrisankar, S., & Natesan, S. (2017). Uniformly convergent numerical scheme for singularly perturbed delay parabolic partial differential equations. International Journal of Computer Mathematics, 94(5), 902-921.Search in Google Scholar
Luo, W. H., Huang, T. Z., Gu, X. M., & Liu, Y. (2017). Barycentric rational collocation methods for a class of nonlinear parabolic partial differential equations. Applied Mathematics Letters, 68, 13-19.Search in Google Scholar
Mirzaee, F., & Alipour, S. (2019). Numerical solution of nonlinear partial quadratic integro-differential equations of fractional order via hybrid of block-pulse and parabolic functions. Numerical Methods for Partial Differential Equations, 35(3), 1134-1151.Search in Google Scholar
Sirignano, J., & Spiliopoulos, K. (2018). DGM: A deep learning algorithm for solving partial differential equations. Journal of computational physics, 375, 1339-1364.Search in Google Scholar
Han, J., Jentzen, A., & E, W. (2018). Solving high-dimensional partial differential equations using deep learning. Proceedings of the National Academy of Sciences, 115(34), 8505-8510.Search in Google Scholar