Write the three matrix coefficients aw aP aE and the rightha

Write the three matrix coefficients (a_w, a_P, a_E) and the right-hand side constant term qp for the following conservation equation discredited in Finite Differences, using Central Differences in space and Crank-Nicolson Scheme in time: partial differential(rho Phi)/partial differential t + partial differential(rho U Phi)/partial differential x = partial differential/partial differential x(Gamma_Phi partial differential Phi/partial differential x)

Solution

in numerical analysisthe crank nicolson method is a finite difference method used for numerically solving the heat equation and similar partial differentil equations.for diffused equation it can be shown the crank nicolosn method is unconditionally stable.for this reason whenever large time steps or high spatial resolution is necessarynthe less accurate backward euler method is often used