It seems to me that Draghilev's method can be applied quite successfully to the solution of Diophantine equations. Here is a simple example where we find two solutions at the intersection line of two ellipsoids:
  x1^2-x1*x2+x2^2+x2*x3+x3^2-961=0;
  (x1-3)^2+10*x2^2+x3^2-900=0;
Solutions: (11, -4, -26) and (10, 1, 29).
 

Based on the text of the program, it is possible to solve various examples with Diophantine equations.
3d_1.mw

Explanations.
f3 is an auxiliary equation for finding the starting point, NPar is a procedure that implements the Draghilev method, the red color of the text is the place where the integer values of the points on the integral curve are filtered.

 Can be compared with the solution of the isolve function
 

 restart:
  f1 := x1^2-x1*x2+x2^2+x2*x3+x3^2-961;
  f2 := (x1-3)^2+10*x2^2+x3^2-900;
  isolve({f1, f2})

Dear all

I construct by hand the two matrices L and U so that A= LU ( LU-factorization) 
I would like to find the number of arithmetic operations required to obtain the matrices 𝐿 and 𝑈

Number_arithmetic_operation.mw

Thank you

Dear all 
I have Sol=proc(  )
local .... ;
RES:=vector with size fixed 
for k from 1 to 100  # iteration
a:=..
if a < 0.1 then 
break;
end if ;
RES[k]:=a;
end do;
print(RES);
 end proc;

My questions:
1) How can I define the vector RES with no size fixed ( we can not at the begin fix the size of RES)
2) Then how can I plot this vector versus number of iteration  
Thank you

Dear all

My code give me the following error 
Error, (in SOR) invalid left hand side in assignment
I don't understand its origin.

coore_invalid.mw

Thank you

Dear all

I have the following code, that solves a linear system 
But I get the error 

Error, (in rtable/Sum) invalid arguments

code.mw

Thank you for any help 

Dear colleagues,

how can i plot streamlines and isothermes and also 3D graphes of Nussult number and skin friction coefficient for boundary layer flow problem with Maple? 

Regards

MAXR

Modified.mw

3D plots of nusselt number like:

Streamline like:

Dear all

How can I solve the system of equations with unknowns  c[2] and Z

system_eqs.mw

Maybe the question can be solved by hand.

thanks

Dear all

I need your help to plot

1)   First:  a three dimensionl curve, that is plot F(X,Y), where X, Y, and F(X,y) is given  

curve_three_d.mw

2) Second: can plot all the curves in the same graph ( 2-dimensional curve)  obtained from the following idea 
for j from 0 by 5 to 40
plot( F(X,j), X)
end for

thank you for your help

For a long time I could not understand how to make a kinematic analysis of this device based on the coupling equations (like here). The equations were drawn up relative to the ends of the grips (horns), that is, relative to the coordinates of 4 points. That's 12 equations. But then only a finite number of mechanism positions take place (as shown by RootFinding[Isolate]). It turns out that there is no continuous transition between these positions. Then it is natural to assume that the movement can be obtained with the help of a small deformation. It seemed that if we discard the condition of a constant distance between the midpoints of the horns (this is the f7 equation at the very beginning), then this will allow us to obtain minimal distortion during movement. In fact, the maximum distortion during the movement was in the second decimal place.
(It seemed that these guys came to a similar result, but analytically "Configuration analysis of the Schatz linkage" C-C Lee and J S Dai
Department of Tool and Die-Making Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan Department of Mechanical Engineering, King’s College, University of London, UK)
The left racks are input.


The first text is used to calculate the trajectory, and the other two show design options based on the data received.
For data transfer, a disk called E is used.
Schatz_mechanism_2_0.mw
OF_experimental_1_part_3_Barrel.mw
OF_experimental_1_part_3.mw

How to integrate the below function from 0 to eta.

A := P(eta)+S(H-2*`cos&theta;`(eta+1)*F)+`cos&theta;`*(2*F(eta)-2*H*F) = S(eta+1)*`sin&theta;`*F(theta)-`sin&theta;`(F*H(theta)-H*F(theta)+F(theta, eta))

Thanks in advance

HI, I have numerically solved the given problem using the dsolve command But I want to solve the same problem using the Differential transformation method.
Can anyone help me to get the series solution for the given problem using DTM.

I want to compare the numerical results with DTM results when lambda =0.5.

eqn1 := diff(f(eta), `$`(eta, 3))+f(eta)*(diff(f(eta), `$`(eta, 2)))-(diff(f(eta), eta))^2-lambda*(diff(f(eta), eta)) = 0.

eqn2 := diff(theta(eta), `$`(eta, 2))+f(eta)*(diff(theta(eta), eta))*Pr = 0

Bcs := (D(f))(0) = 1, f(0) = 0, (D(f))(infinity) = 0, theta(0) = 1, theta(infinity) = 0;

[lambda = .5, Pr = 6.3]

Dear all

I need to  `Put markers to emphasize the point of intersection between f, and g

iteration.mw

thank you

x := [0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4]

y := [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4]
z := [0, 0, 0, 0, 0, 0, .689376362, 1.378752724, 2.068129087, 2.757505449, 0, 1.02920355, 2.0584071, 3.087610649, 4.116814199, 0, 1.216469264, 2.432938529, 3.649407793, 4.865877057, 0, 1.325720912, 2.651441823, 3.977162735, 5.302883646]

How to plot the contour plot for the given data

Hello!

How do I solve this system? could someone help me please.

restart;
eqns := {x(t+1) = (1+10^(-6)*(0.4e-2-0.6e-2)/(0.1e-3))*x(t)+0.7e-1*10^(-6)*y(t),

y(t+1) = 0.6e-2*10^(-6)*x(t)/(0.1e-3)+(1-0.7e-1*10^(-6))*y(t)};

with:
x(0) = 1
y(0) =
y(0) = 857.1428571

Download SystemRecursive.mw