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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.



this question about midpoint method I need help with the part c



i wanted a taylor series  of the expression sin(xy) my code;

mtaylor(sin(x*y),[x=1,y=2],6); and it worked like a charm


now i need to plot the darn thing. so i tried to use tayplot function but i get nothing. is there a special package i need to use tayplot etc..?

im trying to input a number between 0-100 and have the operation return the grade a,b,c,d,f. etc though long i though this might work.

local a,b,c,d,f;
if x=(100..89.5) then
if x=(89.4..79.5)then
if x=(79.4..69.5) then
if x=(69.4..59.5) then
if x=(59.4..0) then

count the number of primes less than using an if-then statement.  Implement your code where j goes from 2 to 15. 

im at a loss i need a little nudge in the right direction.

we use modern computer algebra books

i) computer the GSO of (22,11,5),(13,6,3),(-5,-2,-1) belong to R^3.

ii)trace algorithm 16.10 on computer a reduced basis of the lattice in Z^3 spanned by the vectors form(i).

trace also the values of the d_i and of D, and compare the number of exchange steps to the theoretical upper bound from section 16.3


we use Modern Computer Algebra

let f=x^15-1 belong to Z[x]. take a nontrivial factorization f≡gh mod 2 with g,h belong to Z[x] monic and of degree at least 2. computer g*,h* belong to Z[x] such that   f≡g*h* mod 16 ,deg g*=deg g, g*≡g mod 2.

show your  intermediate. can  you guess some factors of f in Z[x]?


we use Modern Computer Algebra book  

trace algorithm 15.2 on factoring f=30x^5+39x^4+35x^3+25x^2+9x+2 belong to Z[x].choose the prime p=5003 in step.

Dear all;

Special thanks for all the member who help me in Maple.

My last question is:

Write a maple procedure that solves for y(1) in the initial value problem y'(x)=f(y), y(0)=1

using a Numerical stencil based on the n^{th] order taylor series expansion of y.

The procedure arguments include an arbitrary function f, an integrer n, representing the accuracy of the taylor series expansion, and N representing the number of steps between x=0 and x=1.




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

Dear all,

I need to compute the error, How to define the error between the exact and approximation.


                              --- y(x) = -y(x)
                               y(x) = exp(-x)


I have a problem in this code, my goal is to compute the error between the approximate solution obtained by RK3 and Exact  and E ( approximation by RK3).

How to definie the error and prouve that the error is O(h^4)  ( with one step) and the global error is O(h^3).

Thank you  for helping me.




hi everybody

I want to solve this system of equations


while t varies from 0 to 1 by 0.0001 interval. Using newton raphson method, the inital value for each step is the result of the previous step for y,z,p. the very initial values are y=1,z=1,p=1

please help me. Thanks

Dear all

Is there any one can help me to find  the Maple code to solve ODE : y'(x)=f(x,y(x))  using n-step  Adams-Moulton Methods.

The code exist  with mathematica in this link:

there is also the code of this method with Matlab, see please:


But I want ( with maple)

Thank you very much for helping me.







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 $x = a + nh$.       
\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 $i \geqslant 2$
             $$ y[i] = y[i-2] + 2h f(x[i],y[i]); \quad \quad x[i] = a + i h.$$


 Midpoint-Method=proc(f,a,b, N)


 for n from 2 to N do
    x[n] := a+n*h;
    y[n+1] = y[n-1] +  2h f( x[n], y[n] );
// 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.





Rewrite the code that counts the number of primes less than using an if-then statement.  Implement    your code where j goes from 2 to 15.

for i from 2 to 10
while ithprime(j)<2^i do
                        2048, primes = 9

I need to edit this code to satisfy a IF then Statement. can any one help me out?


regards "Geordi"

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