System of Equations with For loop and symbols

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Ryan Mulligan 2020-4-23

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https://ww2.mathworks.cn/matlabcentral/answers/520086-system-of-equations-with-for-loop-and-symbols

评论： Ryan Mulligan 2020-4-24

sym T
C = .2;
N = 6;
gamma = .1;
delR = (1-C)/N;
Ri = C+(i-1)*delR;
A = sym(zeros(N+1));
B = sym(zeros(N+1,1));
for i = 2:N
    
    A(i,:) = ((1/delR^2-1/(Ri*2*delR)))*T(i-1)-((2/delR^2)+gamma^2)*T(i)+((1/delR^2)+(1/(Ri*2*delR)))*T(i+1)==0;
    [A,B] = equationsToMatrix([A(i,:)],[T(i,:)]);
end
X = linsolve(A,B)

This is currently what I have written, I'm trying to solve a system of equations where using information provided by the user, C,N,gamma, it will use the formula displayed by what A(i,:) is equal to to create a system of equations and will then solve for the values of T_0 to T_N. I was able to solve the system without the for loop but cannot seem to figure out how to do it with the for loop. I'm sure there are many mistakes in this code, I'm seeking any sort of guidance I can get. I'm stuck on an error with the symbols, "Undefined function 'T' for input arguments of type 'double' ". Any sort of help would be apprecitated greatly.

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Ryan Mulligan 2020-4-23

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okay so I found some mistakes I belive I made before and wrote a new script, maybe this might help me explain it...

N = 5;
C = .2;
gamma = sqrt(10);
i = [2:N];
delR = (1-C)/N;
Ri = C+(i-1)*delR;
syms a b c d e f
eq0 = a-1==0;
eq1 = (((1/delR^2)-(1/(Ri(:,1)*2*delR))*a))-((2/delR^2+gamma^2)*b)+((1/delR^2+(1/(Ri(:,1)*2*delR))*c))==0;
eq2 = (((1/delR^2)-(1/(Ri(:,2)*2*delR))*b))-((2/delR^2+gamma^2)*c)+((1/delR^2+(1/(Ri(:,2)*2*delR))*d))==0;
eq3 = (((1/delR^2)-(1/(Ri(:,3)*2*delR))*c))-((2/delR^2+gamma^2)*d)+((1/delR^2+(1/(Ri(:,3)*2*delR))*e))==0;
eq4 = (((1/delR^2)-(1/(Ri(:,4)*2*delR))*d))-((2/delR^2+gamma^2)*e)+((1/delR^2+(1/(Ri(:,4)*2*delR))*f))==0;
eq5 = d - 4*e + 3*f ==0;
[A,B] = equationsToMatrix([eq0,eq1,eq2,eq3,eq4,eq5],[a,b,c,d,e,f]);
X = linsolve(A,B)
% a = t1 b = t2 c = t3 d = t4 e = t5 f = t6
% eq0 is given by the fact that t1 or a = 1
% eq5 is given by a choice of three formulas to choose from
% eq1-4 is given from the original equation
%6 unknowns and 6 formulas
%need to make eq1 through eq5 a for loop where eqs 1 through 4 are used for
%i values 2 through N and eq 5 is going to be conditionaly selcted based on
%a value entered by user, either 1 2 or 3 
%this should give us values when solved of theta_1 through N
%for this script N, C, and gamma were chosen.
%Ri is also based on values of i

So since i starts at 2 and goes to N the T0 i refered to earlier should not exist and neither should T7. every row between the first and last is given by the first formula I posted. row 1 is given by t1 = 1 and the last row is given by a choice of three formulas based on if the user enters a 1,2 or 3. So eq 5 will be changing from case to case.