References
[1] Ureña, F., Gavete, L., Garcia, A., Benito, J. J., & Vargas, A. M. (2019). Solving second order non- linear parabolic PDEs using generalized finite difference method (GFDM). Journal of Computational and Applied Mathematics, 354, 221-241.
[2] Saleem, S., and Aziz, I., & Hussain, M. Z. (2020). A simple algorithm for numerical solution of nonlinear parabolic partial differential equations. Engineering with Computers, 36(4), 1763-1775.
[3] Akter, S. I., Mahmud, M. S., Kamrujjaman, M., & Ali, H. (2020). Global spectral collocation method with Fourier transform to solve differential equations. GANIT: Journal of Bangladesh Mathematical Society, 40(1), 28-42.
[4] Polyanin, A. D., & Zaitsev, V. F. (2003). Handbook of Nonlinear Partial Differential Equations: Exact Solutions, Methods, and Problems. Chapman and Hall/CRC.
[5] Friedman, A. (2008). Partial differential equations of parabolic type. Courier Dover Publications.
[6] Lieberman, G. M. (1996). Second order parabolic differential equations. World scientific.
[7] Ladyženskaja, O. A., Solonnikov, V. A., & Uralceva, N. N. (1988). Linear and quasi-linear equations of parabolic type (Vol. 23). American Mathematical Soc.
[8] Ali, H., Kamrujjaman, M., & Islam, M. S. (2020). Numerical computation of FitzHugh-Nagumo equation: Anovel Galerkin finite element approach. International Journal of Mathematical Research, 9(1), 20-27.
[9] Jain, M. K., Jain, R., & Mohanty, R. (1992). Fourth-order finite difference method for 2D parabolic partial differential equations with nonlinear first-derivative terms. Numerical Methods for Partial Differential Equations, 8(1), 21-31.
[10] Kim, D., & Proskurowski, W. (2004). An efficient approach for solving a class of nonlinear 2D parabolic PDEs. International-Journal of Mathematics and Mathematical Sciences, 17, 881-889.
[11] Dehghan, M. (2004). Application of the Adomian decomposition method for two-dimensional parabolic equation subject to non-standard boundary specifications. Applied mathematics and computation, 157(2), 549-560.
[12] Nurwidiyanto, N., Ghani, M. (2022). Numerical results and stability of ADI method to two- dimensional advection-diffusion equations with half step of time. PRISMA, Prosiding Seminar Nasional Matematika, 5, 773-780.
[13] Borcea, L., Druskin, V., Mamonov, A. V., & Zaslavsky, M. (2014). A model reduction approach to numerical inversion for aparabolic partial differential equation. Inverse Problems, 30(12), 125011.
[14] Bhrawy, A. H., Abdelkawy, M. A., & Mallawi, F. (2015). An accurate Chebyshev pseudospectral scheme for multi-dimensional parabolic problems with time delays. Boundary Value Problems, 2015(1), 1-20.
[15] Beneš, M., & Kruis, J. (2018). Multi-time-step domain decomposition and coupling methods for nonlinear parabolic problems. Applied Mathematics and Computation, 319, 444-460.
[16] Guo, X., Shi, B., & Chai, Z. (2018). General propagation lattice Boltzmann model for nonlinear advection-diffusion equations. Physical Review E, 97(4), 043310.
[17] Fu, Z.-J., Tang, Z.-C., Zhao, H.-T., Li, P.-W., & Rabczuk, T. (2019). Numerical solutions of the coupled unsteady nonlinear convection-diffusion equations based on generalized finite difference method. The European Physical Journal Plus, 134(6), 1-20.
[18] Ali, I., Haq, S., Nisar, K. S., & Arifeen, S. U. (2021). Numerical study of 1D and 2D advection-diffusion-reaction equations using Lucas and Fibonacci polynomials. Arabian Journal of Mathematics, 10(3), 513-526.
[19] Lima, S. A., Kamrujjaman, M., & Islam, M. S. (2020). Direct approach to compute a class of reaction-diffusion equation by a finite element method. Journal of Applied Mathematics and Computing, 4(2), 26-33.
[20] Yousefi, S. (2009). Finding a control parameter in a one-dimensional parabolic inverse problem by using the Bernstein Galerkin method. Inverse problems in science and engineering, 17(6), 821-828.
[21] Yousefi, S., Barikbin, Z., Dehghan, M. (2012). Ritz-Galerkin method with Bernstein polynomial basis for finding the product solution form of heat equation with non-classic boundary conditions. International Journal of Numerical Methods for Heat & Fluid Flow, 2012.
[22] Sun, Z., Carrillo, J. A., & Shu, C.-W. (2018). A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials. Journal of Computational Physics, 352, 76-104.
[23] Ali, H., & Kamrujjaman, M. (2022). Numerical solutions of nonlinear parabolic equations with Robin condition: Galerkin approach. TWMS Journal of Applied and Engineering Mathematics, 12(3), 851-863.
[24] Kestler, S., Steih, K., & Urban, K. (2016). An efficient space-time adaptive wavelet Galerkin method for time-periodic parabolic partial differential equations. Mathematics of Computation, 85(299), 1309-1333.
[25] Alam, M., & Islam, M. S. (2019). Numerical solutions of time dependent partial differential equations using weighted residual method with piecewise polynomials. Dhaka University Journal of Science, 67(1), 5-12.
[26] 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.
[27] Lima, S. A., Kamrujjaman, M., & Islam, M. S. (2021). Numerical solution of convection–diffusion– reaction equations by a finite element method with error correlation. AIP Advances, 11(8), 085225.
[28] Ali, H., & Islam, M. S. (2017). Generalized Galerkin finite element formulation for the numerical solutions of second order non-linear boundary value problems. GANIT: Journal of Bangladesh Mathematical Society, 37, 147-159.
[29] Busch, K., Koenig, M., & Niegemann, J. (2011). Discontinuous Galerkin methods in nanophotonics. Laser & Photonics Reviews, 5(6), 773-809.
[30] Li, X., & Li, S. (2021). A fast element-free Galerkin method for the fractional diffusion-wave equation. Applied Mathematics Letters, 122, 107529.
[31] Wu, Q., Liu, F., & Cheng, Y. (2020). The interpolating element-free Galerkin method for three- dimensional elastoplasticity problems. Engineering Analysis with Boundary Elements, 115, 156-167.
[32] Ali, H., Kamrujjaman, M., & Islam, M. S. (2022). An Advanced Galerkin Approach to Solve the Nonlinear Reaction-Diffusion Equations with Different Boundary Conditions. Journal of Mathematics Research, 14(1).
[33] Kanwal, A., Phang, C., & Iqbal, U. (2018). Numerical solution of fractional diffusion wave equation and fractional Klein–Gordon equation via two-dimensional Genocchi polynomials with a Ritz–Galerkin method. Computation, 6(3), 40.
[34] Nadukandi, P., Oñate, E., & Garcia, J. (2010). A high-resolution Petrov–Galerkin method for the 1 Dconvection–diffusion–reaction problem. Computer methods in applied mechanics and engineering, 199, 525-546.
[35] Lai, W., & Khan, A. (2012). Discontinuous Galerkin method for 1D shallow water flows in natural rivers. Engineering Applications of Computational Fluid Mechanics, 6(1), 74-86.
[36] Li, X., & Dong, H. (2021). An element-free Galerkin method for the obstacle problem. Applied Mathematics Letters, 112, 106724.
[37] Abo-Bakr, R. M., Mohamed, N. A., & Mohamed, S. A. (2022). Meta-heuristic algorithms for solving nonlinear differential equations based on multivariate Bernstein polynomials. Soft Computing, 26(2), 605-619.
[38] Lewis, P. E. & Ward, J. P. (1991). The finite element method: principles and applications. Addison-Wesley Wokingham.
[39] Anton, H., Bivens, I. C., & Davis, S. (2021). Calculus: Early Transcendentals. John Wiley & Sons.
[40] Reddy, J. N. (2014). An Introduction to Nonlinear Finite Element Analysis Second Edition: with applications to heat transfer, fluid mechanics, and solid mechanics. OUP Oxford.
[41] Mohamed, N. (2019). Solving one-and two-dimensional unsteady Burgers’ equation using fully implicit finite difference schemes. Arab Journal of Basic and Applied Sciences, 26(1), 254-268.
[42] Mittal, R., & Tripathi, A. (2015). Numerical solutions of two-dimensional Burgers’ equations using modified Bi-cubic B-spline finite elements. Engineering Computations.
[43] Jianchun, L., Pope, G. A., & Sepehrnoori, K. (1995). A high-resolution finite-difference scheme for nonuniform grids. Applied mathematical modelling, 19(3), 162-172.
[44] Ngondiep, E. (2022). A novel three-level time-split approach for solving two-dimensional nonlinear unsteady convection-diffusion-reaction equation. J.Math.Comput.Sci., 26(3), 222-248.