Dear all;

Please Have some one an idea to transform or convert 2nd order ODE to system of First ODE ( of course using maple).

Thanks

Dear All,

I have a simple question, Thanks of your remarks

I would like to find the slope of a line:

I Want to find the slope of this line. How????

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

Dear All,

I have a simple question I try to find the Fourrier Series of:

 f(x)=x*e^{I*x}

with maple or without maple.

Thanks

Dear all,

here, I propose two methods for Adams Moulton Methos, but which one can I used.

The n-step Adams Moulton method to solve y'(x)=F(x,y(x)) is defined by the stencil

y(x+h)=y(x)+h *sum_{j=-1}^{n-1} beta_j F( x-j*h, y(x-j*h) ) + O(h^{n+2})

I want a procedure with single argument ''n'' that calculates and return the ''beta_i'' coefficients

I get two Methods. Which one correspond to my question please, and I don't understand the procedure proposed.

For me; the first give the iterative schemae used, but don't return the vector coefficients ( beta_i) and this methode method an interpolation of the function.

The second method, there is a function f, how this function is maded, and the same for the matrux A and the vector b...

the First Method:

> Adamsmoulton := proc (k::posint)

local P, t, f, y, n;

P := interp([t[n]+h, seq(t[n]-j*h, j = 0 .. k-2)], [f[n+1], seq(f[n-j], j = 0 .. k-2)], x);

y[n+1] = y[n]+simplify(int(P, x = t[n] .. t[n]+h))

end proc;

Second Method:

f:=proc(x,y) if x =0 and y=0 then 1 else x**y fi end;

n:=3; A:=matrix(n,n,(i,j)->f(1-j,1-i));

b:=vector(n, i->1/i);

linsolve(A,b);