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.

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!

1.which rules or theorems can guide to generate relations for words in group theory?

2.Is topological method such as complexes the direction to answer Question 1?

I am running a set of diffrential equation , but i receive below error

"Error, (in LL) cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up"

I can't understand the problem

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?

which method i input a series of random number it output a periodic waveform

Hello dear all,

I use maple 16, x64. When I run this code:

Student[Calculus1][ApproximateInt](cos(y/(-1+y)), y = 0 .. 1, method = lower, iterations = 1)

it results in "0.0667344650", exactly equal with the result of executing

Student[Calculus1][ApproximateInt](cos(y/(-1+y)), y = 0 .. 1, method = lower, iterations = 10000000000)

Any idea?

Best regards

i understand quotient group is

G/(normal subgroup)

= G composite with inverse permutation group of normal subrgoup

is this understanding correct?

If do not have subgroup or normal subgroup, how to do quotient group?

if i shift second row many times in order to find Subgroup satisfy G*Subgroup = Subgroup*G

after find Subgroup then test

inverse(g)*Subgroup*g = Subgroup

how to test whether inverse(g)*Subgroup*g belong to Subgroup?

or just use equal in inverse(g)*Subgroup*g = Subgroup?

a*b - b*a    where a , b are permutation group

how to minus this?

if a + b , then how to plus permutation group

assume the word equation is

a_i *a_j - a_j *a_i = 0

how to find which permutation group is a_i and a_j

my understanding is to try all rotations

a book use underscript i and j

can i see them as upper script for i rotations which is shift i times to left for second row

and try all combination and composite them in two for loop? 

Given a 2x2 matrix I am struggling to write a function that would return a list (a,b, a1, a2) of 2 complex numbers followed by 2 vectors such that the set of the 2 vectors is a basis for CxC and also Ab1=ab1, Ab2=Bb2 if these exist

Any ideas would be greatly appreciated

Good afternoon sir.

I am working on problems related to functions which require dynamic geometry program or

the Geometers sketch pad. I request to you to kindly suggest me with regard to the above cited query.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

Dear all;

Thanks ifor looking and help me in my work. Your remarks are welcome.Description:
 This routine uses the midpoint method to approximate the solution of
     the differential equation $y'=f(x,y)$ with the initial condition $y = y[0]$
     at $x = a$ and recursion starting value $y = y[1]$ at $x = a+h$.  The values
     are returned in $y[n]$, the value of $y$ evaluated at $x = a + nh$.       
                                                                          
Arguments:     
\begin{itemize}
\item  $f$  the integrand, a function of a two variables
                
                \item $y[]$ On input $y[0]$ is the initial value of $y$ at $x = a$, and $y[1]$
                is the value of $y$ at $x = a + h$,
                \item on output for $i \geqslant 2$
             $$ y[i] = y[i-2] + 2h f(x[i],y[i]); \quad \quad x[i] = a + i h.$$
             \end{itemize}

 
CODE USING MAPLE

 Midpoint-Method=proc(f,a,b, N)

h:=(b-a)/N;
x[0]:=a;
y[0]:=1:

 for n from 2 to N do
    x[n] := a+n*h;
    y[n+1] = y[n-1] +  2h f( x[n], y[n] );
od:
// Generate the sequence of approximations for the Improved Euler method
data_midpoint := [seq([x[n],y[n]],n=0..N)]:
//write the function;
F:=(t,y)-> value of function ;

//Generate plot which is not displayed but instead stored under the name out_fig for example
out_fig := plot(data_midpoint,style=point,color=blue)

Your remarks.

Thanks

Let a(1)=916 , a(2)=935 , a(3)=713  , a(4)=845  , a(5)=274  , a(6)=914 ,a(7)=255 . Find formula a(n)= ? ,n=1,2,3,....

I am a new user of Maple. Could anyone help me to know how to call a Maple function/procedure from a Matlab program with a simple example? And conversely, how to call a Matlab function from Maple.