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(Solved): (a) In solving a particular problem, the following coefficient matrix has been obtained: (15) [[2 ...
(a) In solving a particular problem, the following coefficient matrix has been obtained: (15)
[[2 0.1\Delta x^(2),-1,0,0,0,0,0,0],[-1,2 0.1\Delta x^(2),-1,0,0,0,0,0],[0,-1,2 0.1\Delta x^(2),-1,0,0,0,0],[vdots,vdots,vdots,vdots,vdots,vdots,vdots,0],[vdots,vdots,vdots,vdots,vdots,vdots,vdots,vdots],[vdots,vdots,vdots,vdots,-1,2 0.1\Delta x^(2),-1,vdots],[0,0,0,0,0,-1,2 0.1\Delta x^(2),-1],[0,0,0,0,0,0,-1,2 0.1\Delta x^(2)]](i) Mention whether the direct or iterative approach is recommended for solving the above system. (ii) If iterative approach is to be used, determine the required condition for the above system to converge. (iii) Formulate the general convergence criterion for the solution of a system of equations with iterative approach.
