How can I solve system of 6 equations in series?

How can I solve system of 6 equations in series?

[Torsten]

What are the unknowns ?

[Shreen El-Sapa]

A_n, B_n, C1_N, C2_N, D1_n,D2_n= 6 unknowns where n number of convergent point I need to get B_n at n=2

[Sam Chak]

Attempt to sharpen blurry equations.

a = imread('ss.png');
b = imsharpen(a, Radius=2, Amount=1);
imshow(b)
title('Sharpened Image');

[Walter Roberson]

Much of the time, equations involving infinite sums are not solvable through any automated system.

Answer 1

[Torsten]

There is no summation over i in (5.10) and (5.11) although C_n^i and D_n^i are present. Is this a mistake ?

If you want to stop summation at n = 2, you have a linear system of equation in the 6 unknowns. Write your system as M*[A_2, B_2, C1_2, C2_2, D1_2,D2_2] = rhs with a 6x6 matrix "M" and a 6x1 vector "rhs" and solve for [A_2, B_2, C1_2, C2_2, D1_2,D2_2] by using sol = M\rhs .

[Shreen El-Sapa]

yes, a mistake because sum over i means two constant to C and D

[Shreen El-Sapa]

n should be stoped at covergence of series not at 2 I need the position of B2 to get the drag force in terms of this constant

[Torsten]

If n >2, don't you have more unknowns than equations ?

Aren't A_2, A_3,....,A_n, B_2,B_3,...,B_n, C_2^1,C_2^2, C_3^1,C_3^2,...,C_n^1,C_n^2,D_2^1,D_2^2, D_3^1,D_3^2,...,D_n^1,D_n^2 unknown (thus 6*(n-1) unknowns), but you only have 6 equations ?

[Shreen El-Sapa]

yes number of equations depend on number of N

[Torsten]

yes number of equations depend on number of N

What is N ? What are the additional equations apart from the 6 equations you posted ?

Anyway:

If you have a linear system of equations with (number of unknowns) = (number of equations), you can use "linsolve" or "backslash" to solve it:

https://uk.mathworks.com/help/matlab/ref/linsolve.html

If you have a nonlinear system of equations with (number of unknowns) = (number of equations), you can use "fsolve" to solve it:

https://uk.mathworks.com/help/optim/ug/fsolve.html

[Shreen El-Sapa]

function solveSixEquations
% Initial guesses for the variables
initial_guess = ones(6,1); % Assume initial guesses as 1 for all variables
% Call fsolve to solve the system of equations
options = optimoptions('fsolve', 'Display', 'iter');
[solution, fval, exitflag] = fsolve(@equations, initial_guess, options);
% Display the solution
disp('Solution:');
disp(solution);
end
function F = equations(vars)
% Define variables
x1 = vars(1);
x2 = vars(2);
x3 = vars(3);
x4 = vars(4);
x5 = vars(5);
x6 = vars(6);
% Define the system of equations
F(1) = equation1(x1, x2, x3, x4, x5, x6);
F(2) = equation2(x1, x2, x3, x4, x5, x6);
F(3) = equation3(x1, x2, x3, x4, x5, x6);
F(4) = equation4(x1, x2, x3, x4, x5, x6);
F(5) = equation5(x1, x2, x3, x4, x5, x6);
F(6) = equation6(x1, x2, x3, x4, x5, x6);
end
function res = equation1(x1, x2, x3, x4, x5, x6)
% Define your first equation here
res = x1 + x2 - x3; % Example equation
end
function res = equation2(x1, x2, x3, x4, x5, x6)
% Define your second equation here
res = x2 * x4 - x5; % Example equation
end
function res = equation3(x1, x2, x3, x4, x5, x6)
% Define your third equation here
res = x3^2 + x4 - x1; % Example equation
end
function res = equation4(x1, x2, x3, x4, x5, x6)
% Define your fourth equation here
res = x1*x5 + x2*x6 - 1; % Example equation
end
function res = equation5(x1, x2, x3, x4, x5, x6)
% Define your fifth equation here
res = x4^2 + x5*x6 - 2; % Example equation
end
function res = equation6(x1, x2, x3, x4, x5, x6)
% Define your sixth equation here
res = x1 + x2 + x3 + x4 + x5 + x6 - 10; % Example equation
end

[Torsten]

Is there a question left or is this just the way you want to solve the original problem ?