(2) Conservatively discretize in space the 2D nonlinear diffusion equationdu = V· (D(u)Vu) = d_(D(u)d,u) + ô,(D(u)d,u)with second-order accurate central differences with AxAyh. SetUiju(xi, Y;) and DijD(u(xi, Yj)). You may use values of u and D ati, i ±, j, j± . (Keep the time derivative in du-we are deriving thesemi-discrete problem here. Then any of our standard timestepping methodsfor parabolic PDES can be applied.)

Given that, ∂tu=∇Du∇u=∂xDu∂xu+∂yDu∂yu

(2) Conservatively discretize in space the 2D nonlinear diffusion equation Əu = V• (D(u)Vu) = d_(D(u)dµu) + dg(D(u)d,u) with second-order accurate central differences with Ax Ay h. Set || Uij u(xi, Y;) and Dij D(u(xi, Y;)). You may use values of u and D at i, i ±, j, j ±. (Keep the time derivative in du-we are deriving the semi-discrete problem here. Then any of our standard timestepping methods for parabolic PDES can be applied.)

(2) Conservatively discretize in space the 2D nonlinear diffusion equation Əu = V• (D(u)Vu) = d_(D(u)dµu) + dg(D(u)d,u) with second-order accurate central differences with Ax Ay h. Set || Uij u(xi, Y;) and Dij D(u(xi, Y;)). You may use values of u and D at i, i ±, j, j ±. (Keep the time derivative in du-we are deriving the semi-discrete problem here. Then any of our standard timestepping methods for parabolic PDES can be applied.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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