In MATLAB, there are 3 kinds of solver to solve nonlinear equations: fsolve, fmincon and lsqnonlin.
SOLVE NONLINEAR DIFFERENTIAL EQUATION SYSTEMS IN MATLAB HOW TO
We are going to show how to solve this problem via using MATLAB, Fortran, Python and R.Ĭlick to see Source Code MATLAB: fsolve, fmincon and lsqnonlin ($\sigma \in $) Our final goal, we want to figure out the dynamic relationship of $\epsilon^d$, $\epsilon^c$, $\theta$, $alpha$ $\sim$ $\sigma$. It should be emphasized that we also regard $\sigma$ as a variable. The functions $u$, $h_s$ and $h_n$ are defined as: Parameters and functions $F(x)$ and $q (\theta)$ are stated as follow: For example, if we want to solve $\epsilon^d$, $\epsilon^c$, $\theta$ and $alpha$ from the system of nonlinear equations as follow: In most cases, the system of nonlinear equations that we would like to solve is really complicated that we can not even guess how the analytical solution could be. Thus initial condition is really important for solving system of nonlinear equations. Which one to be chosen depends on the initial condition. When there are string type of data in parameters, we can use cell instead of vector. $\alpha$, $\beta$, $\lambda$, $\gamma$ are numerical data.
To input parameters $\alpha$, $\beta$, $\lambda$, $\gamma$ into myfun, we can use para vector or global command in MATLAB.
The system of nonlinear equations can be written into myfun.m as follow: myfun.m 1į( 1) = alpha*(x+ 1)*(x -3)* exp( beta*y) į( 2) = lambda*(y -5)*(y+ 7)* exp( gamma*x) $\alpha$, $\beta$, $\lambda$, $\gamma$ are parameters. Most of the time, the system is so complex that we can not solve it analytically but only numerically.Īssume there is a simple system of nonlinear equation:Īnd we need to solve it numerically. Solving the nonlinear equations can give us the clues of the behavior of a nonlinear system. Nonlinear System is a system in which the change of the output is not proportional to the change of the input, which can modeled with a set of nonlinear equations.
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