Homework Discussion 2

# Homework Discussion 2 - 1 Homework Discussion 2 Computer...

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Unformatted text preview: 9/13/2011 1 Homework Discussion 2 Computer Problems 10.1.4, 10.1.7, 10.2.4, RK45, RK45_Adaptive 10.1 9/13/2011 2 10.1.4 function rval = problem4b() n=100; a=0; b=1; h = (b-a)/n; t=a; x=1; for k=1:n x1=(1+t)^(-1)*x; x2=(-1)*(1+t)^(-2)*x + (1+t)^(-1)*x1; x3=2*(1+t)^(-3)*x + (-2)*(1+t)^(-2)*x1 + (1+t)^(-1)*x2; x4=(-6)*(1+t)^(-4)*x+(-2)*(1+t)^(-3)*x1 + ... (-3)*(1+t)^(-2)*x2 + (1+t)^(-1)*x3; x5=24*(1+t)^(-5)*x + 4*(1+t)^(-3)*x2 + ... (-4)*(1+t)^(-2)*x3 + (1+t)^(-1)*x4; x=x+h*(x1+(1/2)*h*(x2+(1/3)*h*(x3+... (1/4)*h*(x4+(1/5)*h*(x5))))); t=a+k*h; end rval = x; end function rval=problem4a() n=100; a=0; b=1; h=(b-a)/n; t=a; x=0; for k=1:n x1=1 + x^2; x2=2*x*x1; x3=2*x1^2 + 2*x*x2; x4=6*x1*x2 + 2*x*x3; x5=6*x2^2 + 8*x1*x3 + 2*x*x4; x=x+h*(x1+(1/2)*h*(x2+(1/3)*h*(x3+... (1/4)*h*(x4+(1/5)*h*(x5))))); t=a+k*h; end rval=x; end 10.1 9/13/2011 3 Solution • Given ′ = with = 1 . We have ′′ = ′ + , ′′ = 1 ′′′ = ′′ + 2 ′...
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Homework Discussion 2 - 1 Homework Discussion 2 Computer...

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