Based on the following algebraic equations: and the condition for convergence: W

Question

Based on the following algebraic equations: and the condition for convergence: Write out the central point coefficient, ap, and neighbor point coefficients, anb, for the following two cases and then determine which case will converge and which one will diverge Case 1: 2 Phi1 = 0.1 Phi2 + 1.1 Phi3 + 1.4 3 Phi2 = 1.5 Phi1 -2.9 Phi3 +0.9 4 Phi3 = 2.2 Phi 1 + 1.8 Phi 2 + 2.8 Case 2: 4 Phi1 = 3 Phi2 + 0.7 Phi3 + 2.6 3 Phi2 = 1.2 Phi1 + 0.6 Phi3 + 3.8 2 Phi3 = 1.5 Phi1 -0.5 Phi2 + 0.9 Converge Diverge

Explanation / Answer

Case I - Diverge Case II - Converge This is because of the nature of equations, and their algebraic solution.

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