TY - JOUR AU - Ganon, Ardjouma AU - Taha, Manin Mathurin AU - Koffi, N'guessan AU - Toure, Augustin Kidjegbo PY - 2021 TI - Numerical blow-up for nonlinear diffusion equation with neumann boundary conditions JO - Journal of Nonlinear Sciences and Applications SP - 80--88 VL - 14 IS - 2 AB - This work is concerned with the study of the numerical approximation for the nonlinear diffusion equation \( (u^{m})_t= u_{xx}, \ 00 \), under Neumann boundary conditions \( u_x(0,t)=0, \ u_x(1,t)=u^{\alpha}(1,t), \ t>0 \). First, we obtain a semidiscrete scheme by the finite differences method and prove the convergence of its solution to the continuous one. Then, we establish the numerical blow-up and the convergence of the numerical blow-up time to the theoretical one when the mesh size goes to zero. Finally, we illustrate our analysis with some numerical experiments. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.014.02.03 DO - 10.22436/jnsa.014.02.03 ID - Ganon2021 ER - TY - JOUR TI - On the numerical quenching time at blow-up AU - K. A. Adou AU - K. A. Touré AU - A. Coulibaly JO - Adv. Math. Sci. J. PY - 2019 DA - 2019// VL - 8 ID - Adou2019 ER - TY - JOUR TI - Remarks on blow-up behavior for a nonlinear diffusion equation with neumann boundary conditions AU - K. Deng AU - M. X. Xu JO - Proc. Amer. Math. Soc. PY - 1999 DA - 1999// VL - 127 ID - Deng1999 ER - TY - JOUR TI - Numerical quenching for heat equations with coupled nonlinearboundary flux AU - K. B. Edja AU - K. N'guessan AU - B. J.-C. Koua AU - K. A. Touré JO - Int. J. Anal. Appl. PY - 2019 DA - 2019// VL - 17 ID - Edja2019 ER - TY - JOUR TI - Numerical Blow-up for the Porous Medium Equation with a Source AU - R. Ferreira AU - P. Groisman AU - J. D. Rossi JO - Numer. Methods Partial Differential Equations PY - 2004 DA - 2004// VL - 20 ID - Ferreira2004 ER - TY - JOUR TI - The Balance bet we en Nonlinear Inwards and Outwards Boundary Flux for a Nonlinear Heat Equation AU - R. Ferreira AU - F. Quirós JO - J. Differential Equations PY - 2002 DA - 2002// VL - 184 ID - Ferreira2002 ER - TY - JOUR TI - Diffusivity versus Absorption through the Boundary AU - J. Filo JO - J. Differential Equations PY - 1992 DA - 1992// VL - 99 ID - Filo1992 ER - TY - JOUR TI - Blow-up for Semidiscretization of Semilinear Parabolic Equation With Nonlinear Boundary Condition AU - A. Ganon AU - M. M. Taha AU - A. K. Touré JO - J. Math. Res. PY - 2019 DA - 2019// VL - 11 ID - Ganon2019 ER - TY - JOUR TI - Numerical blow-up on whole domain for a quasilinear parabolic equation with nonlinear boundary condition AU - A. Ganon AU - M. M. Taha AU - A. K. Touré JO - Adv. Math. Sci. J. PY - 2020 DA - 2020// VL - 9 ID - Ganon2020 ER - TY - JOUR TI - Numerical method of estimating the blow-up time and rate of the solution of ordinary differential equations--An application to the blow-up problems of partial differential equations AU - C. Hirota AU - K. Ozawa JO - J. Comput. Appl. Math. PY - 2006 DA - 2006// VL - 193 ID - Hirota2006 ER - TY - JOUR TI - Blow-Up Analysis for a Nonlinear Diffusion Equation with Nonlinear Boundary Conditions AU - Z. X. Jiang AU - S. Zheng AU - X. F. Song JO - Appl. Math. Lett. PY - 2004 DA - 2004// VL - 17 ID - Jiang2004 ER - TY - JOUR TI - Numerical blow-up time for a parabolic equation with nonlinear boundary conditions AU - K. C. N'dri AU - K. A. Touré AU - G. Yoro JO - Int. J. Numer. Methods Appl. PY - 2018 DA - 2018// VL - 17 ID - N'dri2018 ER - TY - JOUR TI - On the Approximation of Blow-up Time for Solutions of Nonlinear Parabolic Equations AU - T. K. Ushijima JO - Publ. Res. Inst. Math. Sci. PY - 2000 DA - 2000// VL - 36 ID - Ushijima2000 ER -