Question

3. A nonlinear system: In class we learned how to use Taylor expansion up to the 1* order term to solve a system of two non-linear equations; u(x.y)- 0 and v(x.y)-0. This method is also called Newton-Raphson method. (a) As we did in lecture, expand u and v in Taylor series up to the 1st order and obtain the iterative formulas of the method. (In the exam you should have this ready in your formula sheet). 1.2) as an initial guess y=-x2 + x +0.75 y+5xyx (c) Calculate the relative approximate error for both x and y. (d) Substitute your results of the first iteration into the equations and report the discrepancy in the right hand side between vour substitution and the original eauation. (e) Plot the two equations using ezplot MATLAB function. From the plot estimate the solution of the system

Answer 1

0 5866 0 2258 43 8

3(X2A)-3G.sas r43, o.ozgo 521つ2.12, 4

Matlab code for ezplot clear all close all syms x Y f(x,y,-x . ^ 2-x-0.75+y; g(x,y)=x ."2-5.*x.*y-y; hold on ezplot (f) ezplot (g) title 'ezplot for x amd y) xlabel ( ·x' ) ylabel('y 용욤욤응용음 음 응용음 End of Code 응용음음응용음음용용 ezplot for x amd y -2 -4 -6 Published with MATLAB R2018a

%Matlab code for ezplot
clear all
close all

syms x y
f(x,y)=x.^2-x-0.75+y;
g(x,y)=x.^2-5.*x.*y-y;

hold on
ezplot(f)

ezplot(g)

title('ezplot for x amd y')
xlabel('x')
ylabel('y')

%%%%%%%%%% End of Code %%%%%%%%%%