Solve Nonlinear Equations with MATLAB

MATLAB solves nonlinear equations either symbolically or numerically with solvers such as "fsolve". This example demonstrates how to obtain a solution to sets of nonlinear equations.

[@agihtiassalam8628]

as a beginer in MATLAB, your lectures are very helpful, short and very compact. keep it up ! thank you

[@borislum1998]

you are good teacher, easy to follow

[@enriquenieto100]

Thank you !!! Well and simply explained

[@amrgaber4400]

Man I love you, I tried to solve some combustion equations using solve but got error then I tried your method with fsolve and worked❤️❤️

[@apm]

Thanks for the feedback. I'm glad it worked!

[@davidtorres9922]

Thank you men, you save me. Very useful video!!!

[@hussain55019]

Love You Sir..

[@kilziantoine9542]

Hello, is it possible to add the constraints on z(1) and z(2) (or x & y ) in fsolve similarly to what you did in the solve function ?

[@apm]

I'd recommend fmincon for constrained solutions to nonlinear equations. See this page (example #2): apmonitor.com/che263/index.php/Main/MatlabOptimization

[@apm]

Fsolve can't handle inequalities. Fmincon is a good tool for constrained nonlinear programming.

[@pamirkldis118]

thanks a lot, you are the best

[@Reyarth100]

I need to solve a system of parametric non linear equations. How can I do that? Thanks!

[@apm]

+Reyarth100, take a look at the nonlinear regression example here: apmonitor.com/che263/index.php/Main/MatlabDataRegression

[@dsrabelo]

thank you!

[@albertbii5315]

good explanation.

[@erikbryson7353]

Thank you.

[@aaaaaa6285]

How to solve a system of 10 nonlinear equation with 10 variables, having parameters that must be calculated by another function and imported?

[@apm]

You can have any number of variables and equations with this approach. apmonitor.com/che263/index.php/Main/MatlabSolveEquations You may also want to look at Gekko if you need to solve a large-scale problem (10,000+ variables) apmonitor.com/che263/index.php/Main/MatlabCallsPython

[@ebeb9156]

Very nice, thank u

[@onyiboemmanuel6060]

Thanks a lot Sir

[@AdrianaCastilloC]

Thank you sooo much!

[@jossiaradasilvabarbosa3537]

Thank you

[@hojoduurenbileg5681]

Could you explain why you don't give the Myfunctions function any arguments when you put it into the fsolve.

[@rrc]

At 6:05, the fsolve function only needs two inputs. They are the function handle (or string name) and the initial guesses (second argument). If you have optional input arguments that are not accessible to fsolve to change then you'll pass those in with the anonymous function such as fsolve(@(z)myFunction(z,optional_args),zg). If you don't have any optional arguments then you can just leave off the input arguments because fsolve knows that the inputs should be the same size as zg (the guess values).

[@hojoduurenbileg5681]

Oh alright. Thanks.

[@kapilgadhave2432]

thanks

[@witsqafa]

how to solve the root 2 with 4 iteration and the starting point is also define?

[@apm]

+Witsqa Fadhilah, for finding the roots to a polynomial, I'd suggest the polyroot function. If you need to code it yourself, a Newton's method should work.

[@saddamhussainsoomro2810]

sir can you help me to solve 12 non linear equations with 12 variables, or guide anything please. Thanks

[@apm]

Check out APM MATLAB or Python Gekko. They can solve these problems. You can also find tutorials at apmonitor.github.io/data_science/

[@samianina6636]

Hi saddam, I have a similar task here. I have to solve 16 non linear equations with 16 unknowns using lsqnonlin in Matlab (my variables are constrained) could you please advice how did you solve for yours? Thanks.

[@ram.4152]

How to solve a system of non linear equations with different constant values that is read from a Csv file

[@apm]

Here is information on reading data from a CSV file: apmonitor.com/che263/index.php/Main/PythonDataAnalysis and solving nonlinear equations: apmonitor.com/pds/notebooks/10_solve_equations.html The syntax for MATLAB is similar, but you could also try it in Python.

[@muhammadaaqibrabbani777]

Sir could it solve for an unkown constant like c instead of 9?

[@apm]

Yes, it isn't a problem if c has a value. If you need a symbolic solution then there is a symbolic toolbox. Otherwise, here is a symbolic tutorial in Python: github.com/APMonitor/data_science/blob/master/10.%20Solve_Equations.ipynb

[@WytseZ]

Thanks for the explanation, very clear! Possible improvement for your video; Use some de-essing software because it is very painful to listen now

[@apm]

Thanks for the suggestion. I did upgrade my microphone a couple years ago and that has greatly helped the sound quality.

[@WytseZ]

@@apm Good to know!

[@arpitamondal5110]

i wanted to solve 2 coupled nonlinear equations but i'm getting "equation solved , solver stalled". could you help me out?

[@apm]

Here is some help for solving differential equations: apmonitor.com/pdc/index.php/Main/SolveDifferentialEquations

[@arpitamondal5110]

@@apm thanks but i cant handle ......"Equation solved, solver stalled. fsolve stopped because the relative size of the current step is less than the value of the step size tolerance squared and the vector of function values is near zero as measured by the value of the function tolerance." how can i fix this?

[@apm]

@@arpitamondal5110 it appears that the solver reaches an area that is causing a problem but that the solver nearly reached a solution. One suggestion is to try a better initial guess. You can also try a different solver when you use Python Gekko or Python fsolve: apmonitor.com/che263/index.php/Main/PythonSolveEquations One advantage of Python gekko is that you can add additional information such as an objective function (m.Minimize(x)) to create a unique solution if the problem has degenerate equations or additional degrees of freedom. You can also specify constraints with Gekko to help the solver avoid problem areas.

[@arpitamondal5110]

@@apm thanks a lot 🙂...I'll try

[@khaoulabriki4220]

Thank you it is very helpful . if you can make a video to solve a nonlinear boundary equation ex:q = x''[t] + x'[t] + x[t] + x[t]^3;

[@apm]

Here is some course content on second order systems: apmonitor.com/che436/index.php/Main/LectureNotes20 or apmonitor.com/pdc/index.php/Main/SecondOrderSystems

[@khaoulabriki4220]

APMonitor.com Thank you very much

[@adchrisrob]

U DA REAL MVP

[@apm]

Thxs!

[@danielcachafeiro2590]

Shouldnt you get as many roots as grades the polynomials are?

[@apm]

Numerical methods typically only get one solution and it depends on the starting guess value.

[@ikhsanerlingga]

What does the equal sign mean?

[@apm]

The equal sign means that it is an equality constraint where the expression on the left side must equal the expression on the right side. Does that answer your question?

[@user-qe6xd9oc5p]

Do I have to write that x is greater than zeor

[@apm]

You need to use an optimizer to add constraints. apmonitor.com/che263/index.php/Main/MatlabOptimization

[@SaqrThabet]

that was an impeccable lesson, but [x,y]=solve([x^2+y^2 = = 20,y = = x^2],x>0,y>0,[x,y]) did not work properly with me. However [x,y]=solve('x^2+y^2=20', 'y=x^2', ,'x>0' , 'y>0' ) did work just fine.

[@apm]

Thanks for posting your solution. There was an update to the package in a later version. From the documentation: www.mathworks.com/help/symbolic/solve.html : Character vector inputs have been removed. Instead, use syms to declare variables and replace inputs such as solve('2*x == 1','x') with solve(2*x == 1,x).

[@chinnychin0135]

how do you split the z?

[@apm]

It shows how to do that at 6:22 It is x=z(1) and y=z(2)

[@rebekah3632]

how is x>0 ?

[@apm]

That is one of the constraints on the variable.

[@mannobilli458]

how we solve z=sinx in matlab plz reply me soon

[@apm]

+Manno Billi, I don't think I understand your question. You can type something like z=sin(3.14) or you can plot the sine function with x=linspace(0,6.28) plot (x,sin(x)) Let me know if you have a more specific question.

[@mannobilli458]

use matlab to to make calculations if x=10 and y=3 solve z=sinx this is question written in textbook i want to how we write these calculations in matlab

[@apm]

Hummm...the question still doesn't make sense. There appear to be two given values (x and y) that are either fixed parameters or else guess values. I'm not sure what "z" is in this case. Here is the best way that I can interpret you question. Let me know if this isn't what you are asking. Perhaps you are asking if y = sin(x) and y=0, determine the value of x. The solution is with fsolve as: fsolve(@sin,0.1) or with cosine: fsolve(@cos,0.1) The 0.1 value is a guess value. The solution to the first one is 0.0 and the solution to the second one is pi/2 (although additional solutions exist. There is no solution if y = 3 because sin(x) cannot be higher than +1.0.

[@mannobilli458]

suppose that x=-7-5i and y=4+3i.use matlab to compute x/y

[@apm]

Here are some commands: x = -7 -5*i y = 4+3*i x/y Are these homework problems?

[@SebasTian-xx6yc]

who were from engineering computations 2019

[@apm]

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