Guest co-blogger: Luis Serrano

Many students ask me how do I do this or that in MATLAB. So I thought why not have a small series of my next few blogs do that. In this blog, I show you how to solve a nonlinear equation that needs to be set up.

For example to find the depth ‘x’ to which a ball is floating in water is based on the following cubic equation

4*R^3*S=3*x^2*(R-x/3)

where

R= radius of ball

S= specific gravity of ball

So how do we set this up if S and R are input values?

The MATLAB program link is here.

The HTML version of the MATLAB program is here.

**DO NOT COPY AND PASTE THE PROGRAM BELOW BECAUSE THE SINGLE QUOTES DO NOT TRANSLATE TO THE CORRECT SINGLE QUOTES IN MATLAB EDITOR.****DOWNLOAD THE MATLAB PROGRAM****INSTEAD**

%% SUMMARY

% Language : Matlab 2018b;

% Authors : Autar Kaw and Luis Serrano;

% Mfile available at

% http://nm.mathforcollege.com/blog/NonlinearEquations_withSetUp.m;

% Last Revised : January 22, 2020;

% Abstract: This program shows you how to solve a nonlinear equation

% that needs to set up as opposed that is just given to you.

clc

clear all

%% INTRODUCTION

disp(‘ABSTRACT’)

disp(‘ This program shows you how to solve’)

disp(‘ a nonlinear equation that needs to be setup’)

disp(‘ ‘)

disp(‘AUTHORS’)

disp(‘ Autar Kaw and Luis Serrano’)

disp(‘ ‘)

disp(‘MFILE SOURCE’)

disp(‘ http://nm.mathforcollege.com/blog/NonlinearEquations_withSetUp.m’)

disp(‘ ‘)

disp(‘LAST REVISED’)

disp(‘ January 22, 2020’)

disp(‘ ‘)

%% INPUTS

% Solve the nonlinear equation where you need to set up the equation

% For example to find the depth ‘x’ to which a ball is floating in water is based on the following

% cubic equation 4*R^3*S=3*x^2*(R-x/3) R= radius of ball S= specific gravity of ball So how do we set this up if S and R are input values

S=0.6

R=0.055

%% DISPLAYING INPUTS

disp(‘INPUTS’)

func=[‘ The equation to be solved is 4*R^3*S=3*x^2*(R-x/3)’];

disp(func)

disp(‘ ‘)

%% THE CODE

% Define x as a symbol

syms x

% Setting up the equation

C1=4*R^3*S

C2=3*x^2*(R-x/3)

f=C1==C2

% Finding the solution of the nonlinear equation

soln=vpasolve(f,x);

solnvalue=double(soln);

%% DISPLAYING OUTPUTS

disp(‘OUTPUTS’)

for i=1:1:length(solnvalue)

fprintf(‘\nThe solution# %g is %g’,i,solnvalue(i))

end

disp(‘ ‘)

________________________

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- Holistic Numerical Methods Open Course Ware:
- Numerical Methods for the STEM undergraduate at http://nm.MathForCollege.com;
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