## Problem with piecewise function?...

I've been poking around with convolutions on Maple, and some weird behavior came up---if I let it compute the convolution of a piecewise function, then take the convolution of that, it comes out differently than if I enter a function from scratch as the middle step---file attached (PiecewiseProblem.mw).  I'm not really a Maple pro, so am I'm doing something crazy here?

Thanks!

## Plot Error of ODE. ...

Dear all,

h: stepsize;

x in [0,x0];

I give all the step of my code, but I think there is a mistake. I wait for your Help.

I would like to compute the error between  Method Huen with step size h and step size 2h using the definition of epsilon given below:

## The error written epsilon(x0,h)= sqrt(1/(N+1) * sum_i=0^N  (y_i^{2h}-y_(2i)^h)^2 ), where y_i^(2h) is the approximation of y(i*2*h).

## We want : loglog epsilon versus h.

f:=(x,y)=1/(1+cos(y));

ode:=diff(y(x),x)=f(x,y);

ic:=y(0)=1;  h:=x0/(2*N);

## Method Heun with step size 2h

> Heun1 := proc (f, x0,)

local x, y, i, h, k;

y := Array(0 .. N);

x := Array(0 .. N);

h := evalf((1/2)*x0/N);

x[0] := 0;

y[0] := 1;

for i from 0 to N do

x[i+1] := (2*i+2)*h;

k[1] := f(x[i], y[i]);

k[2] := f(x[i]+h, y[i]+h*k[1]);

y[i+1] := y[i]+h*((1/2)*k[1]+(1/2)*k[2]);

end do;

[seq([x[i], y[i]], i = 0 .. N)];

end proc;

### Now Heun with step size h  ( the same h)

> Heun2 := proc (f, x0,)

local x, y, i, h, k;

y := Array(0 .. N);

x := Array(0 .. N);

h := evalf((1/2)*x0/N);

x[0] := 0;

y[0] := 1;

for i from 0 to N do

x[i+1] := (i+1)*h;

k[1] := f(x[i], y[i]);

k[2] := f(x[i]+h, y[i]+h*k[1]);

y[i+1] := y[i]+h*((1/2)*k[1]+(1/2)*k[2]);

end do;

[seq([x[2*i], y[2*i]], i = 0 .. N)];

end proc;

## simplify(-ln(x)+ln(y),size)...

Hi There,

Could you let me know how to tell Maple to use the ln simplification to give -ln(x)+ln(y) = ln(y/x).

I tried following command.

simplify(-ln(x)+ln(y), ln)

However, it is not able to give the required simplification.

## Numerica Dsolve for Boundary values problem...

Hi,

I wrote the following code which is properly run

restart:

# parametrs

MUR:=(1-phi)^2.5:
RhoUR:=(1-phi+phi*rho[p]/rho[f]):
RhoCPR:=(1-phi+phi*rhocp[p]/rhocp[f]):
BetaUR:=(phi*rho[p]*beta[p]+(1-phi)*rho[f]*beta[f])/(RhoUR*rho[f])/beta[f]:

dqu3:=diff(h(x),x\$1)-RhoUR*BetaUR*T(x);
dqu2:=5*diff(T(x),x\$2)+k[f]/k[nf]*Pr*RhoCPR*f(x)*diff(T(x),x\$1);
dqu1:=5/(MUR)*diff(f(x),x\$3)
+ 2*(diff(h(x),x\$1)*x-h(x))
+RhoUR*(3*f(x)*diff(f(x),x\$2)-diff(f(x),x\$1)^2);
rho[f]:=998.2: cp[f]:=4182: k[f]:=0.597:   beta[f]:= 2.066/10000:
rho[p]:=3380: cp[p]:=773: k[p]:=36:   beta[p]:= 8.4/1000000:

k[nf]:=((k[p]+2*k[f])-2*phi*(k[f]-k[p]))/((k[p]+2*k[f])+phi*(k[f]-k[p])):
rhocp[nf]:=rho[p]*cp[p]*phi+rho[f]*cp[f]*(1-phi):
rhocp[p]:=rho[p]*cp[p]:
rhocp[f]:=rho[f]*cp[f]:

phi:=0.00:
binfinitive:=6: Pr:=7: lambda:=0:

with(plots):
pppe:=dsolve( {dqu1=0,dqu2=0,dqu3=0,T(0)=1,T(binfinitive)=0,f(0)=0,D(f)(0)=lambda,D(f)(binfinitive)=0,h(binfinitive)=0}, numeric );
-pppe(0);
print(odeplot(pppe,[x,diff(f(x),x)],0..binfinitive,color=black,numpoints=400));
print(odeplot(pppe,[[x,diff(f(x),x)]],0..binfinitive,color=black,numpoints=400));
print(odeplot(pppe,[[x,T(x)]],0..binfinitive,color=black,numpoints=400));

However, in some range of parameters, I must increase the value of binfinitive (for example binfinitive=50). however, my code is doesnt converge for higher values of 10 (at most). Can anyone change this algorithm in a way that it insensitive to the value of binfinitive?

Amir

## How to export a figure to .emf format file...

I plot a curve with "plot" command, how to export the figure to .emf format file?

## Can you use solve for multiple data points?...

Hi, the title isn't great as I didn't know how to describe this really. I need to solve the following equation for b:

y = (1-exp(-x*b))/(1-exp(-50*b))

When I put a value for y in, this is fine and fsolve gives me a numeric real solution. However, even when using RealDomain, it does not give me a real solution if I leave y as it is, and instead gives a 'RootOf' solution, which I don't really understand. This is the same whether using solve or isolate:

b=-(1/50)RootOf(_Zx-50ln(-y+ye^(_Z)+1))

I have the values of x and y for multiple data points and can put them in an nx1 matrix. Is there a way to replace x and y with matrices (with real numbers in) and solve for each set of points for b (ie there would be n values of b)? Obviously I could go through and put in each value of x and y but this would take ages, so was just wondering if there's a quick way to do this.

I have tried by simply putting matrices instead of the letter but get the error:

Error, invalid input: exp expects its 1st argument, x, to be of type algebraic, but received Vector(50, {(1) = -50*b, (2) = -49*b,...

James

## Is there a way to test a problem if it fails or do...

I suppose you would have to programme this, because I couldn't find anything relating to vector spaces in my Maplesoft Linear Algebra tutor or package.

My question really is, you have a problem like, the set of all pairs of real numbers of the form (1,x) with the operations (1,y)+(1,y')=(1,y+y') and k(1,y)=(1,ky)

( ^ taken straight out of my homework haha)

and you run through the 10 vecctor space axioms to determine whether it fails and it not a vector space, or it passes all and it is a vector space.

Is there a way to do this in Maplesoft?

## differential equations +plot scale...

Hell

I write this code and didn't work , I have some erorrs as

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)
Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

also I have question " How I can change the scale of plot"

parameters := [z = 0, Omega = 2.2758, tau = 13.8, T2 = 200, omega0 = 1, r = .7071, s = 2.2758, H = 1.05457173*10^(-34), omega = .5, k = 1666666.667, Delta = 1.7758]

sys1 := {diff(u(t), t) = s*v(t)-u(t)/T2, diff(v(t), t) = -s*u(t)-2*Omega*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(kz-`&omega;t`)*w(t)-v(t)/T2, diff(w(t), t) = 2*Omega*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(kz-`&omega;t`)*v(t)}; ICs1 := {u(-20) = 0, v(-20) = 0, w(-20) = -1}

ans1 := dsolve(`union`(eval(sys1, parameters), ICs1), numeric, output = listprocedure); plots:-odeplot(ans1, [[t, u(t)], [t, v(t)], [t, w(t)]], t = -20 .. 20, legend = [w, v, u])

U := eval(u(t), ans1); F := eval(((-2*10^33*Omega*H*r*U(t))*(1/omega0^2))*exp(-r^2/omega0^2-t^2*1.177^2/tau^2)*cos(kz-`&omega;t`), parameters)

plot(F, t = -20 .. 20)

## How do I solve a differential equation system in M...

Hi,

Please help me in solving system consist the three differential equations with three unknowns. I did already a few attempts, but I can not finish. Once in the final result was got RootOf and do not know what to do. I tried also numerically. I very very ask for some suggestions: (

with the boundary condition

parameters A,B,C are constans

1)

qa1 := A1*(diff(Tg(x), x, x))+A2*(diff(Tg(x), x))+(A3+A4)*Tg+A3*Tz+A4*Tw = 0;

eqa2 := B1*(diff(Tw(x), x, x))+B2*(diff(Tw(x), x))+(B3+B4)*Tw+B3*Tz+B4*Tg = 0;

eqa3 := C1*(diff(Tz(x), x, x))+(C3+C4)*Tz+C3*Tg+C4*Tw = 0

2)

On paper, the system of three equations with three unknowns I changed to system of two equations with two unknowns but still nothing.

A[1] := 2,

eqa1 := A[1]*C[1]*(diff(z(x), x, x, x, x))/C[3]+A[2]*C[1]*(diff(z(x), x, x, x))/C[3]+(A[1]*C[3]+A[1]*C[4]+A[3]*C[1]+A[4]*C[1])*(diff(z(x), x, x))/C[3]+(A[1]*C[3]+A[1]*C[4])*(diff(z(x), x))/C[3]+(A[3]*C[3]+A[3]*C[4]+A[4]*C[3]+A[4]*C[4]+A[3]*C[3])*z(x)/C[3]+A[1]*C[4]*(diff(y(x), x, x))/C[3]+A[2]*C[4]*(diff(y(x), x))/C[3]+(A[3]*C[4]+A[4]*C[4]+A[4]*C[3])*y(x)/C[3] = 0;

eqa2 := B[4]*C[1]*(diff(z(x), x, x))/C[3]+(B[4]*C[3]+B[4]*C[4]+B[3]*C[3])*z(x)/C[3]+B[1]*(diff(y(x), x, x))+B[2]*(diff(y(x), x))+(B[4]*C[3]+B[4]*C[4]+B[3]*C[3])*y(x)/C[3] = 0;

row := eqa1, eqa2;

sol := dsolve({row}, {y(x), z(x)});

Thank you very much for your help.

Ewa.

## A straight line in 3D...

Dear Maple users,

i have a set of 2 Lines: L1 (determined by the intersection of plane x + y -1=0 and plane x - z - 1=0),

L2 ( intersection of plane x + y-7=0 and plane x-y+1 = 0 ).

which functions or commands of maple should I use "visualize" those 2 lines L1 and L2?

JJ

## HFfloat(undefined)...

Hallo guys,

I am newbie in Mapple, i could not solve the problem yet, here is my little function. I want to estimate beta with the Maximum Likelihood Estimation with Weibull:

> MaximumLikelihoodEstimate(Weibull(beta, eta), F1); F1 := Vector([1500, 1750, 2250, 4000, 4300, 5000, 7000]);
print(`output redirected...`); # input placeholder
[beta = HFloat(HFloat(undefined)), eta = HFloat(HFloat(undefined))

]

May someone help me why i just get HFloat(undefined)  ?

Kind regards

## Solve This Equation...

Can anyone tell me how to solve the equation above using Maple.  I know that there is a solution around x=0.995, y=0.743, but I cannot induce Maple to find it.  Any help or suggestions would be appreciated.

Ratch

## How to tell Maple not to expand derivatives....

I'm simplifying this Reynolds Equation starting from here:

Reynolds:=Diff(p(x)*h(x)^3/(12*mu)*Diff(p(x),x),x)-u(x)/2*Diff(p(x)*h(x),x)+Diff(p(x)*h(x)^3/(12*mu)*Diff(p(x),z),z)=Diff(p(x)*h(x),t):

Then I apply the dchange command:

dchange({p(x)=P(X)*Pa,x=Lx*X,h(x)=H(X)*h2},Reynolds,{P,h,X,u,H});

The problem is that it expands the new derivatives and I need the equation in its compact form.

How do I tel Maple only to make the substitution but not to expand the result?

I know that it expands by default, can I modify that?

## How to export large Matrix, sequence, Array data t...

In ode solve command i generated a large array data. The output shows a large order matrix of this form

[110001x6 Matrix

Datatype:Anything

Storage:rectangular

order:Fortran_order].

I want to export this matrix into a notepad. Which can then be used for plotting in TecPlot.

Looking for good response

## Optimization Homework Help...

I want to begin by saying hello! im new to the forums i hope some one can give me a push in the right direction with some of my maple homework. im sort of stuck on a few of these questions and would be greatfull for some help.

Let .

a) Let g be the tangent line to f when x = c. Use Maple to find g as a function of c.

b) Use Maple to plot f and g(3) using view = [0..5, -25..100].

c) Define a function called plot_tan that plots both f and g(c) where f is blue and g(c) is red. Also use the same view as in part (b). Note that plot_tan is also a function of c.

d) Using your function plot_tan, the following all in one graph using the display command:

plot_tan(1), plot_tan(1.5), plot_tan(2), plot_tan(2.5), plot_tan(3), plot_tan(3.5), plot_tan(4), plot_tan(4.5), plot_tan(5).

e) Try using the option insequence = true in the display command. What does this option do? (You will need to click on the graph and play around with some buttons).

now it seems to me i have to use the point slope formula to get to a fuction g of c. thanks in advance! i hope you can help

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