Consider the following partial differential equation. 20 20 + x t Domain: x varies...

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Consider the following partial differential equation. 2²0 2²0 მი + əx² дуг Ət Domain: x varies from 0 to 1, y varies from 0 to 1 Boundary conditions: at x = 0,0 = 0 at x = 1,0 = 1 at y = 0,0 = 0 at y = 1,0 = 1 2 a. Use finite difference method to discretize the following equations by using central differencing in space and forward differencing in time. At Consider: Ax = Ay and a = Ax I. II. III. = 0 Formulate the discretized equation using explicit method. Formulate the discretized equation using Implicit method. For explicit method formulate the problem in matrix form for 5 points in x and y directions. Consider the following partial differential equation. 2²0 2²0 მი + əx² дуг Ət Domain: x varies from 0 to 1, y varies from 0 to 1 Boundary conditions: at x = 0,0 = 0 at x = 1,0 = 1 at y = 0,0 = 0 at y = 1,0 = 1 2 a. Use finite difference method to discretize the following equations by using central differencing in space and forward differencing in time. At Consider: Ax = Ay and a = Ax I. II. III. = 0 Formulate the discretized equation using explicit method. Formulate the discretized equation using Implicit method. For explicit method formulate the problem in matrix form for 5 points in x and y directions.