Matlab home work 15

Contents

• PROBLEM #1
• PROBLEM #2
• PROBLEM #3

PROBLEM #1

clear,clc

x = linspace(-1,1,11);
y = x.^5 + 2*x.^2 - x + 3;

int_trap = trapz(x,y)
int_quad = quad('x.^5 + 2*x.^2 - x + 3',-1,1)
int_quadl = quadl('x.^5 + 2*x.^2 - x + 3',-1,1)

int_trap =

    7.3600


int_quad =

    7.3333


int_quadl =

    7.3333

PROBLEM #2

clear,clc

syms y(t)
y(t) = dsolve(diff(y,t) == t^2 +y, y(0) == 0)
Y = subs(y(t),t,[0,1])

 
y(t) =
 
2*exp(t) - 2*t - t^2 - 2
 
 
Y =
 
[ 0, 2*exp(1) - 5]
 

PROBLEM #3

clear,clc

syms f(x) h1 h2 h3
h1(x) = f
h2(x) = diff(f,x)
h3(x) = diff(f,x,2)
V = odeToVectorField(2*diff(f,3) == -f*diff(f,2))
M = matlabFunction(V,'vars',{'x','Y'})

sol = ode45(M,[0,1],1)

 
h1(x) =
 
f(x)
 
 
h2(x) =
 
diff(f(x), x)
 
 
h3(x) =
 
diff(f(x), x, x)
 
 
V =
 
           Y[2]
           Y[3]
 -(Y[1]*Y[3])/2
 

M = 

    @(x,Y)[Y(2);Y(3);Y(1).*Y(3).*(-1.0./2.0)]

Index exceeds matrix dimensions.

Error in symengine>makeFhandle/@(x,Y)[Y(2);Y(3);Y(1).*Y(3).*(-1.0./2.0)]



Error in odearguments (line 87)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

Error in ode45 (line 113)
[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

Error in Homework15 (line 28)
sol = ode45(M,[0,1],1)

Published with MATLAB® R2015a