Hi, 

I wish to be able to calculate the roots of the function f(p) by using the roots of the function h(p) and applying the bisection method due to the fact that the roots of h(p) bracket the roots of f(p) as can be seen in the graph below. I have done this before for another example when h:=J₀(p); and hence i could use The commands BesselJZeros(0,n)/BesselJZzeros(0,n+1) to find the roots. So my problem arises with the finding the roots of h(p) and how to insert them into my bisection loop(underlined below).

Any advice would amazing. Many thanks

Download spherical_continue.mw

Download spherical_continue.mw

Hi,

I am trying to plot union of regions in Maple 15. Each region is formed by a set of inequalities. I can see from online such a feature is available in Maple 17.

The code is:

> with(plots);

> I1 := inequal({x < 1, y < 1}, x = 0 .. 2, y = 0 .. 2, optionsfeasible = [color = "Brown", thickness = 2]);

> I2 := inequal({y > 1, x < 1}, x = 0 .. 2, y = 0 .. 2, optionsfeasible = [color = "Yellow", thickness = 2]);

> display(I1);      ---> This is working 

>display(I2);      ---> This is also working

>display({I1,I2});  ---> Not working.

The above is also attached in the worksheet.

Is there any other way to plot the two region. I am new to Maple. Please suggest me the alternative in Maple 15.

Thanks!

Hello there,

i got a question regarding derivatives in Matlab.

I got a function for a example:

f:=f1(y)*f2(x)

from this function i need the partial derivatives with respect to x and y, i can easily get them with

diff(f,x)

diff(f,y)

now i want to compute the derivative of f with respect to time t, assuming that y and x both depend on t - how can i tell maple that y and x depend on t?

thanks

ben

I want to find the solution in a special form.
How can I do it?
Here is what I tried:

(Maple)

(Maple)


In the left hand side u_1 is not changed in  D(u_1).
I want to substitute and evalute (differentiate) it.

Thanks,  Sandor

Dear All;

Happy, to discuss with you these lines, and thank you to help me.

My goal is:

ode := D(y)(x) = f(x,y(x));
                          
In this expression, is assumed to be a known function of the independant variable
                                      x
 and the function that we are trying to solve for
                                    y(x)
.  The simplest numerical stencils to solve this equation will give us an approximation to
                                      y
 at some point
                                  x = X + h
 given some knowledge of
                                      y
 at
                                    x = X
.  All of these stencils are based on the Taylor series approximation for
                                    y(x)
 about
                                    x = X
 to linear order:
eq1 := y(x) = series(y(x),x=X,3);
                       
eq2 := h = x - X;
eq3 := subs(isolate(eq2,x),eq1);
                                
Now, we can remove the first derivative of y
                                     
 by making use of the differential equation:
eq4 := subs(x=X,ode);
eq5 := subs(eq4,eq3);
                           

Now we must compute the same for y(x-h)  and then make.  How can I do this please

assume input 0.567

how to get a list [5, 6, 7] or [5;6;7]?

(a) Design your own 3-stage explicit Runge-Kutta method with one-step error O(h4).

(b) Test your method by solving y′ = −y. Confirm that the global error in your numerical solution

is O(h3).

Write a Maple procedure that solves for y(1) in the initial value problem

                     y′ = f(y),     y(0) = 1,

using a numerical stencil based on the nth order Taylor series expansion of y. The procedure’s arguments should include an arbitrary function f, an integer n representing the accuracy of the Taylor series expansion, another integer N representing the number of steps between x = 0 and x = 1. Pick a test problem and compare your results with the output of dsolve/numeric.

Hello Maplers, i have encountered a little annoyance with Maple, that i would like to ask, whether it can be solved. 

It's when i try to define a function, like f(x)=2x and try to define it with a command f(x):=2x, a pop-up box comes up, asking me whether i'd like to use a 'function definition', or 'remember table assignment', and i would like to make Maple remember my choice that i want a function. 

I know i can write it like f:=x->2x, but i hate to look at that, to be frankly..

So, is there any way to solve this?

Please tell me how to do about the following problem to me.

g:=(b*y)^k*k*y;

simplify(%);

Then, what I obtained was (b*y)^k*k*y, not (b^k)*k*y^(k+1).

expand of the command brought the same answer not (b^k)*k*y^(k+1).

Please tell me what was wrong to my calculation.

Thank you in advance.

Taro.

How to solve this equation

cos(x)^2+2*x*cos(x)-2*sin(x)+4=0

with

solve(%,x) and evalf(%) ?

I get no solution. Is there any option to force Maple to solve this equation by solve and evalf?

Student[Calculus1]:-NewtonsMetnod(%,x=2) solves the problem.
If I use Series for sin(x) and cos(x) Maple can solve it too.

Thank you

Dear all,

A stupid question.

I tried to create a density plot of the data but I only saw the method to plot graphs through equations. (Actually, I'm not very familiar with related statistical commands in Maple)

This is the histograph of my data:

And I want to get the density plot like this:

It seems that we can get the graph through "InteractiveDataAnalysis" but cannot print the graph into the worksheet or assign the graph to the variable.

How to create a density plot through data? Thanks.

AOA... I want to export system of linear equation into matrix form...

Help.mw

restart:

Eq1:=S*diff(f(x,t),x,t)+diff(f(x,t),x)^2-f(x,t)*diff(f(x,t),x$2)=diff(f(x,t),x$3);

BCs := {D[1](f)(0,t)=cos(t), f(0,t)=0,D[1](f)(L,t)=0};

ICs := {f(x,0)=0};

S:=10:L:=5:
smod3:= pdsolve(Eq1,ICs union BCs,numeric,range=0..L);

smod3:-plot(t=0,  color=red):

it seems to me that the problem is due to the mixed bcs. Any way around?

Cheers!

Dear All,

I analyzed some example of linear equation systems and tried to distinguish the difference between the solve and fsolve in these cases.

1. In general case, the deviation between solve and fsolve is less than 10^-8, for example:

But, in some case, the deviation is more than 10^-7, for example:

how to reduce the error of solving the problem by fsolve?

2. It seems that solve will automatically translate the answer into numerical result while the system is composed with decimals, for example, we redo the second case with no decimals:

Is it possible to get the exact solution while the decimal is involved in the system?

The related file is attached. I'd appreciate any help on this topic. Thank a lot.

solve_and_fsolve.mw