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Engineering and Comp Sci Homework Help
Using finite difference to solve DE
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[QUOTE="jdawg, post: 5532172, member: 499239"] [h2]Homework Statement [/h2] d[SUP]2[/SUP]T/dx[SUP]2[/SUP] = 5*(dT/dx) - 0.1*x = 0 T(0) = 50 T(10) = 400 (Δx) = 2[COLOR=#0000b3]I've figured out how to do these problems when Δx = 1, but when it equals any other number it goes wrong. I know you start by plugging in the algebraic approximations for the differential elements, I think maybe my problem is the nodes?[/COLOR] [h2]Homework Equations[/h2] d[SUP]2[/SUP]T/dx[SUP]2[/SUP] = (T[SUB]i+1[/SUB] * T[SUB]i[/SUB] + T[SUB]i-1[/SUB])/([SUP](Δx)[/SUP]) dT/dx = (T[SUB]i+1[/SUB] - T[SUB]i-1[/SUB])/(2*Δx) [h2]The Attempt at a Solution[/h2] node1 = 2; node2 = 4; node3 = 6; node4 = 8; For node1: (T[SUB]2[/SUB] - 2*T[SUB]1[/SUB] + T[SUB]0[/SUB])/(2[SUP]2[/SUP]) + 5*((T[SUB]2[/SUB] - T[SUB]0[/SUB])/(2*2)) - 0.1*(2) = 0 End up with ======> -0.5*T[SUB]1[/SUB] + 1.5*T[SUB]2[/SUB] = 50.2 For node2: (T[SUB]3[/SUB] - 2*T[SUB]2[/SUB] + T[SUB]1[/SUB])/(2[SUP]2[/SUP]) + 5*((T[SUB]3[/SUB] - T[SUB]1[/SUB])/(2*2)) - 0.1*(4) = 0 End up with =======> -T[SUB]1[/SUB] - 0.25*T[SUB]2[/SUB] + 1.5*T[SUB]3[/SUB] = 0.4 For node3: (T[SUB]4[/SUB] - 2*T[SUB]3[/SUB] + T[SUB]2[/SUB])/(2[SUP]2[/SUP]) + 5*((T[SUB]4[/SUB] - T[SUB]2[/SUB])/(2*2)) - 0.1*(6) = 0 End up with ========> -T[SUB]2[/SUB] - 0.5*T[SUB]3[/SUB] + 1.5*T[SUB]4[/SUB] = 0.6 For node4: (T[SUB]5[/SUB] - 2*T[SUB]4[/SUB] + T[SUB]3[/SUB])/(2[SUP]2[/SUP]) + 5*((T[SUB]5[/SUB] - T[SUB]3[/SUB])/(2*2)) - 0.1*(8) = 0 End up with ========> -T[SUB]3[/SUB] - 0.5*T[SUB]4[/SUB] = -724.2 [COLOR=rgb(0, 0, 179)]I put all the coefficients into a matrix and its tridiagonal, which is good I think. But when I try to plot it in MATLAB it gives me a crazy looking zigzag, which I'm pretty sure isn't correct. If someone could point out what I'm doing wrong I would really appreciate it! :)[/COLOR] [/QUOTE]
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Using finite difference to solve DE
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