Hi Viacheslav. Thanks again. I guess that with this new feature SMath must to be very close of version 1.0.

Just a question about derivatives. Yours ode solvers returns n-1 columns for the n-degree differential equation, so: which is the better way to implement y <n> (x) : diff(y(x),x,n) ? Because SMath diff doesn't recognize lspline.

I think in 3 or 4 ways: return n columns for the differential equation of degree n, return functions y'(x), y''(x), ... and y<n>(x) as you do for y(x), a function like lspline(3) but for the derivative (something like dlspline) since cubic splines have information about the derivative or a diff function like matlab's, which simply calculates the difference in the values of a vector, for each column of a matrix.

But the truth is, I don't know which method could be the best, nor do I have any idea what is the best way to obtain the function derived from the result of any of your many solvers at this time.

And one last question: could it be possible to implement the graph of parametric functions in the XY Plot plugin? Something like ParamtricPlot (x (t), y (t), a, b ) and that takes the number of points from the plugin configuration, or ParamtricPlot (x (t), y (t), a, b, N ) for N subdivisions (N + 1 points) of the interval a < t < b.

Best regards.
Alvaro.

It looks pretty good.

In the attached an example about how to add an "extra" column to the ode solver for return the last derivative. In the "traditional" implementation it it is not necessary because it is simply the last component of D (t, Y), the argument function of the solvers for systems of differential equations. But if what you have is the higher-order differential equation, things are no longer so simple.

It also shows how to "sterilize units", an expression that I had never read or heard, but that I am copying from Pompelmo. I think it is an easy and effective way to be able to program functions like nonlinear or ode solvers that accept units.

RK23.sm (72kb) downloaded 26 time(s).
RK23.pdf (341kb) downloaded 24 time(s).

Best regards.
Alvaro.

Edited by user 11 December 2021 10:16:00(UTC)  | Reason: Not specified

Plugin updated.

Changes:

- Adams variable added (allows you to choose a method for the Adams() solver): "AB1".."AB8", "AB5" - default;
- CWD variable value changed.

To calculate the first steps of the method, Runge-Kutta of the 4th order is used, so while the order is not higher than the 5th it makes sense.

Edited by user 15 December 2021 15:50:36(UTC)  | Reason: Not specified

Скажите пожалуйста, можно ли с помощью данного расширения производить символьные расчеты как в Маткаде или только это касается графиков. Пробую посчитать символьно передаточную функцию, задействовал Maple Tools, simplify выдал что-то не то что должен был по моим разумениям. Raschjot17.sm (25kb) downloaded 10 time(s).

Edited by user 17 December 2021 18:41:52(UTC)  | Reason: Not specified

Hi. Notice that SMath does not operate automatically expands matrix operations. Also, the maple's linalg package have some issues too, and sometimes needs to call evalm function, which means "eval as matrix".

If D is a scalar I suppose that the correct result is (2), but if it is a 2x2 matrix I think it is (3).

In both cases you cannot calculate A ^ (- 1) because the second column of A is zero.



Could you comment what is the expression you expect for A? Also perhaps something from this post may be useful to you: https://en.smath.com/for...d-laplace-transform.aspx

Best regards.
Alvaro.

I finally figured out how it works

Mathcad Block. Spring pendulum.sm (49kb) downloaded 43 time(s).

Edited by user 28 December 2021 01:19:04(UTC)  | Reason: Not specified

Plugin updated.

Changes:

- CWD and image processing functions fixed.

P.S. Found a critical issue while trying to resolve this kind of system (x'(t) and x''(t) in one equation):



The conversion of a complex system to a matrix form is not correct. A more complex algorithm is required. Only simple types of ODEs will be computed correctly.

Edited by user 21 June 2022 20:48:22(UTC)  | Reason: Not specified

These ODEs is called the Arenstorf Orbit.

lsoda.Arenstorf Orbit.sm (16kb) downloaded 47 time(s).
lsoda.Arenstorf Orbit.pdf (94kb) downloaded 48 time(s).

The problem is that I use an universal algorithm that independently searches for derivatives in equations and arranges them in a matrix. I started with low order derivatives, so the equations were solved with respect to them first. It's wrong, but it worked in simple cases. When I redid the enumeration of derivatives of higher orders, I found that I did not take into account the case of different naming of variables. In this regard, an incorrect matrix is ​​obtained and the numerical algorithm cannot find a solution.
I need to organize a double loop that first takes into account different variables, and then their derivatives.
It is strange that I didn't do this earlier, because the rest of the code is designed for this.

I had a very simple set of examples that I experimented with. As soon as I tried something more complicated - it immediately revealed the problem.

Edited by user 22 June 2022 08:51:43(UTC)  | Reason: Not specified

Yes I agree, Alvaro. I meant that my algorithm is trying to convert the system of equations into a form that is understandable by numerical solvers. In our case, this is the "general form". I didn't know Maple had special features for this.