Question

Consider the ODE f(x,y) = - 10r5 Take initial conditions xo = 0 , yo = y(0) = 11 , x1 = 0.2 and y y(0.2)= 22, solve for y(99) with a step size of 0.2 using an adaptation of Euler's method, which uses two known y solutions to approximate the next y solution. The general formula is: 3 Vi+2 i+1+ h 1 (owsan-cuea An example of the first few iterations is shown below. (wcomnce) (ceny5-cesn) y2 yh 3 (esa-c) the nearest integer? What is the value of y(99) rounded Answer

Answer 1

Euler method for ode clear all close all %function for ode f-e (x, y) ( (x.^2)./y)-10.*x.*5; initial values y0 11 x0 0; y1-22 xl-0.2 step size h 0.2 x(1)xly1)=yl for i-2:99 y(i)yl+h*((3/2) *f (xl,yl )-(1/2) f(x0 ,y0) ); x(i)-x1+0.2; y0 y1 yl-y(i x0 x1 x1-x(i) end fprintfY (99)= %f.\n',y(end)) 용동동을을동동을을동동을용동 end code of %용동용을몸용용을몸용 -100299 52 1.2940 69 Y(99) Published with MATLAB® R2018a 1

%%Euler method for ode
clear all
close all

%function for ode
f=@(x,y) ((x.^2)./y)-10.*x.^5;

%initial values
y0=11; y1=22;
x0=0; x1=0.2;

%step size
h=0.2;
x(1)=x1;y(1)=y1;

for i=2:99
  
    y(i)=y1+h*((3/2)*f(x1,y1)-(1/2)*f(x0,y0));
    x(i)=x1+0.2;
  
    y0=y1;
    y1=y(i);
  
    x0=x1;
    x1=x(i);
  
end

fprintf('Y(99)= %f.\n',y(end))

%%%%%%%%%%%%%% end of code %%%%%%%%%%%%