maple fan

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11 years, 108 days

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@Rouben Rostamian  wonderful! thank you very much

@ecterrab 

I don't think the nist library can be the standard for mathematical software development.

It's just a basic requirement.

Only standard is market demand.

Although the mupad is weak comparing to maple, but matlab is moving on.

The special functions in mathematica is more than maple in physics.

I noticed maple make a big effort to Physics package.

If Maple want more potential consumers besides math(eg, physics,chemistry,biology,geography,astronomy,and most engineering disciplines), more functions are needed.

eg. zernike polynomials

@Carl Love 

I got it.

plots:-complexplot((-2.0)^x,x=-sqrt(2)..sqrt(2),style=point,gridlines);

This figure solves all my problem.

thanks, my friends.

@Preben Alsholm 

I know there are many branches, but how to find the real root.

I want to see the plot with real root.

@Preben Alsholm 

restart;

Digits:=20:

series((-2.0)^x,x=-1,6);

convert(%,polynom);

p:=expand(%);

x1:=fsolve(Im(p),x,complex);

x2:=fsolve(Im(p),x,complex,avoid={x=x1});

x3:=fsolve(Im(p),x,complex,avoid={x=x1} union {x=x2});

x4:=fsolve(Im(p),x,complex,avoid={x=x1} union {x=x2} union {x=x3});

x5:=fsolve(Im(p),x,complex,avoid={x=x1} union {x=x2} union {x=x3} union {x=x4});

x6:=fsolve(Im(p),x,complex,avoid={x=x1} union {x=x2} union {x=x3} union {x=x4} union {x=x5});

x7:=fsolve(Im(p),x,complex,avoid={x=x1} union {x=x2} union {x=x3} union {x=x4} union {x=x5} union {x=x6});

x8:=fsolve(Im(p),x,complex,avoid={x=x1} union {x=x2} union {x=x3} union {x=x4} union {x=x5} union {x=x6} union {x=x7});

x9:=fsolve(Im(p),x,complex,avoid={x=x1} union {x=x2} union {x=x3} union {x=x4} union {x=x5} union {x=x6} union {x=x7} union {x=x8});

x10:=fsolve(Im(p),x,complex,avoid={x=x1} union {x=x2} union {x=x3} union {x=x4} union {x=x5} union {x=x6} union {x=x7} union {x=x8} union {x=x9});

#It seems like the fsolve command can get infinite root for the poly, but not for the (-2.0)^x.

sols:=solve(Im(p),x);

[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10];

seq(eval(p,x=i),i=%);

seq(eval((-2.0)^x, x=i),i=%%);

seq(eval((-2.0)^x, x=i),i=[sols]);

 

I want the real root, but (-2.0)^x seems like a multi-value function.

Maybe I'm wrong.

Any suggestions is appreciated

 

@rmhmd 

Unfortunately, after nearly 8 years, there is still no options with nonlinearfit that can be used for goodness of fit test.

I think that two short-cuts need to be added.

one is for the repeat last command. In Matlab command window, use the up arrow for that. In Maple worksheet mode, no short cut for it.

the second one is execute the remaining commands which means run commands from the present cusor to the end.

@ Dr. Venkat Subramanian, I understand your method.

Unfortunately, this problem is from an math excises book without answer, I can't give some physical meaning.

But I'll try your advice.

thank you very much for your help.

@ I just want to got the solution curve, but I don't know the time interval at first.

I got some approaches from your method.

thank you for your help

@Preben Alsholm thank you for your help, and also to Dr. Venkat Subramanian.

Use the isolate can get yp2, and then substitute it to eqs[1].

Then use solve&allvalues to get all three roots.

I guess there can be some way to track the root.

I tried but not succeed.

some attempts are below:

restart;
yp2*Y[3]+yp4*Y[2]*sin(Y[1]^2)+cos(yp4*Y[3]) = sin(t), Y[2]*yp4*sin(Y[1]*Y[3])+5*yp2*Y[4]*cos(Y[1]^2)+t^2*Y[1]*Y[3]^2 = exp(-Y[3]^2);
subs(Y[1]=1,Y[2]=1,Y[3]=2,Y[4]=2,t=0,[%]);
isolate(%[2],yp2);
subs(%,%%[1]);
allvalues(solve(%));
fsolve(%%,yp4=2.0);
'evalf(%%[i])'$i=1..3;

@Carl Love Sorry, just my mistakes,but that's don't affect the difficulty of the problem

@Preben Alsholm thank you  for your analysis.

I change the time span 0..40 to 0..1000 and see what happening.

Maple gives Warning, cannot evaluate the solution further right of 739.59941, probably a singularity.

For comparison, I tried this in mma and found that the upper bound can be increased to 10^308, a large number.

It's a difference in numerical solution of ode between the two systems.

@Carl Love Thank you for your help

@Markiyan Hirnyk and Carl, thank you for your help. I got it.

One more question, is there exist a universal method to judge the numerical solution of ode is right?

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