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Dear all;

Than you for help.

how  many steps are required to achieve a error of 1.e-3 in the numerical value of y(1).

Here The 3 -step procedure  Range Kutta Method.

## Exact  solution  

### We will modifty N ( number of steps to get error =10^(-3). )


## Procedure Range Kutta

> RK3 := proc (f, a, b, y0, N)

local x, y, n, h, k, vectRK3;

y := Array(0 .. N);

x := Array(0 .. N);

h := evalf(b-a)/N;

x[0] := a; y[0] := 1;

for n from 0 to N-1 do

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

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

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

k[3] := f(x[n]+h, y[n]+h*(-k[1]+2*k[2]));

y[n+1] := y[n]+(1/6)*h*(k[1]+4*k[2]+k[3])

end do;

[seq([x[n], y[n]], n = 0 .. N)]; y[1];

end proc;

## Now  we compute the error between y(1) and exact  solution for different value of  N

### I have a problem in this part

 errorRk3 := array(1 .. 29);
 for N from  2 to 30 do

errorrRk3[N] := abs(eval(rhs(res), x = 1)-RK3((x,y)->-y,0,1,N));

if errorrRk3[N] =10^{-3} end ;
end  do ;



write a maple package for quaternion must include the following procedures:

1) for quaternion polynomials f, g:  find degree of f , compute f +g ,f-g, fg.

2)for matrices over quarternion polynomials A,B: compute A+B,A-B, AB.

hint using records to represent quaternions.

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
 and the function that we are trying to solve for
.  The simplest numerical stencils to solve this equation will give us an approximation to
 at some point
                                  x = X + h
 given some knowledge of
                                    x = X
.  All of these stencils are based on the Taylor series approximation for
                                    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

(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).

Numerical Method ...

March 04 2014 alshehri 5

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.

Midpoint method ...

March 03 2014 alshehri 5



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..?

display grades operation....

February 27 2014 Dira 20

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

if then statement problem...

February 27 2014 Dira 20

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.




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