Solve a matrix that has nonlinear coefficients

Question

Ali Aykut 2023-10-9

编辑： Torsten 2023-10-9

I am trying to solve a matrix that has the following form,

f(T_n) * T_(n-1) - T_n + f(T_n) * T(n+1) = f(T_n)

How this should be handled?

Answer 1

Torsten 2023-10-9

编辑：Torsten 2023-10-9

If the coefficients contain the unknowns, a matrix representation of your system of equations leads you nowhere.

Write your system of equations in the unknowns T_n as a system of algebraic equations G(T) = 0 and use "fsolve" to solve.

Ali Aykut 2023-10-9

Thank you, I thought there was a way to solve with matrix representation.

Torsten 2023-10-9

编辑：Torsten 2023-10-9

Thank you, I thought there was a way to solve with matrix representation.

The matrix representation of the equations is only useful if the matrix coefficients and the right-hand side are constant.

Sometimes it's necessary to use fixedpoint iteration

T^(i+1) = A(T^i)*T^i + b(T_i) (i: iteration index)

with T = (T(1),...,T(n)) if n is large, but if possible solve A(T)*T + b(T) - T = 0 using "fsolve". This will be much more efficient.