Explanation To plot the solution, the matlab program can be altered slightly as follows: Replace the Adams-Bashforth Two-Step Method with the Three-Step Method, and replace the Adams-Moulton One-Step Method with the Two-Step Method. In addition, order-four Runge-Kutta should be used as a startup method. The approximate solution on [0,2] is indistinguishable from the correct solution in the plot below. %% Adams-Bashworth-Moulton Predictor, corrector and other methods %% initialization %% syms x y % Range of x xspan=[2,3]; % Step size h=0.1 % Initial values y0=3, x0=2 y(1)=y0;x(1)=x0; % No. of steps steps=(xspan(2)-xspan(1))/h; %% Define f(x,y) %% f= @(x,y)x*(y-x); %% Exact Solution %% [Xe,Yexact]=ode45(f,xspan,y0); Xe=Xe(1:4:end); Yexact=Yexact(1:4:end); Exact_Sol=vpa([Xe Yexact],5) %% Euler's Method %% for j=2:steps+1 x(j,1)=x(j-1)+h; y(j,1)=y(j-1,1)+h*f(x(j-1,1),y(j-1,1)); end euler=vpa([x y],5) % Mean Square Error mse = vpa(norm(Yexact-y,2),5) %% Heun's Method %% for j=2:steps+1 x(j,1)=x(j-1)+h; k1(j-1,1)=h*f( x(j-1), y(j-1) ); k2(j-1,1)=h*f( x(j-1)+h, y(j-1)+k1(j-1)); y(j,1)=y(j-1)+0.5*(k1(j-1)+k2(j-1)); end heuns=vpa([x y],5) % Mean Square Error mse = vpa(norm(Yexact-y,2),5) %% RK 4th order method %% for j=2:steps+1 x(j,1)=x(j-1)+h; k1(j-1,1)=h*f( x(j-1), y(j-1) ); k2(j-1,1)=h*f( x(j-1)+h/2, y(j-1)+0.5*k1(j-1) ); k3(j-1,1)=h*f( x(j-1)+h/2, y(j-1)+0...

Numerical Analysis, Books A La Carte Edition (3rd Edition)

3rd Edition

ISBN: 9780134697338

Author: Timothy Sauer

Publisher: PEARSON

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Chapter 6.7, Problem 9CP

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To find out the solution and plot the approximation using Adam-Bash forth 3^r^d step and Adam-Moulton 2- step method with given step size and interval.

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Chapter 6.7, Problem 8CP

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Chapter 6 Solutions

Numerical Analysis, Books A La Carte Edition (3rd Edition)

Ch. 6.1 - Show that the function y(t)=tsint is a solution of...Ch. 6.1 - Show that the function y(t)=esint is a solution of...Ch. 6.1 - Use separation of variables to find solutions of...Ch. 6.1 - Find the solutions of the IVP given by y(0)=0 and...Ch. 6.1 - Apply Eulers Method with step size h=1/4 to the...Ch. 6.1 - Apply Eulers Method with step size h=1/4 to the...Ch. 6.1 - (a) Show that y=tan(t+c) is a solution of the...Ch. 6.1 - (a) Show that y=tanh(t+c) is a solution of the...Ch. 6.1 - For which of these initial value problems on [0,...Ch. 6.1 - Sketch the slope field of the differential...

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To find out the solution and plot the approximation using Adam-Bash forth 3 r d step and Adam-Moulton 2- step method with given step size and interval.

Solution Summary: The author explains how to plot the approximation using Adam-Bashforth 3 r d step, and Adams-Moulton 2-step method. The approximate solution is indistinguishable from the correct solution

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To find out the solution and plot the approximation using Adam-Bash forth 3^r^d step and Adam-Moulton 2- step method with given step size and interval.

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Chapter 6 Solutions

To find out the solution and plot the approximation using Adam-Bash forth 3 r d step and Adam-Moulton 2- step method with given step size and interval.

Solution Summary: The author explains how to plot the approximation using Adam-Bashforth 3 r d step, and Adams-Moulton 2-step method. The approximate solution is indistinguishable from the correct solution

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To find out the solution and plot the approximation using Adam-Bash forth 3rd step and Adam-Moulton 2- step method with given step size and interval.

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Chapter 6 Solutions

To find out the solution and plot the approximation using Adam-Bash forth 3^r^d step and Adam-Moulton 2- step method with given step size and interval.