amirhadiz

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These are questions asked by amirhadiz

Hi everybody

My question comes back to singularities within a differential equation.

Consider a Non-Linear differential equation of y(x), say Eq1.

When we solve this with dsolve ({Eq1, ICs}, type=numeric) we can extract the value of y(x) for each independent variable x.

Now if Eq.1 admits a singularity (for example at x=x0) that can not be removed the following message appears:

Error, (in unknown) cannot evaluate the solution further left (right) of x0, probably a singularity.

By left(right) Maple means that the solution cannot be evaluated for x<x0 (x>x0).

However, in some situations, the Linear form of Eq.1 behaves regularly for all of the values of x, I call the Linear equation as Eq.2.

Now my question is:

How can I make a conditional expression with proc and for commands that do the following requirements: 

1. Detect the singular point x0 by running a loop over x for the numerical solution of Eq.1 and write the value of x0 for different initial conditions , since the value of x0 depends on initial conditions.

2. Find the value of y(x=x0) by solving Eq.2 as the linear equation is no longer singular at x=x0.

I want to find out the suitable algorithm through which I can perform the above procedures.

Thank you very much and best regards.

Hadi

Hi everybody

I have a problem with finding the interpolation function from a data list.

In Mathematica I can find the interpolation function from a set of data simply as below:

data := {{13, -2}, {12, -1}, {11, 0.0}, {10, 1}, {9, 2}, {8, 3}, {7, 
   4}, {6, 5}, {5, 6}, {4, 7}, {3, 8}, {2, 9}, {1, 10}}

g := Interpolation[dat]

Plot[g[x], {x, 1, 9}] (see the attached file for the diagram)

The mathematica software gives simply the interpolating function and then we can work with it.

However, I cannot do the same procedure with maple.

Would you be so kind as to let me know how can I make an interpolating function for these set of data in maple?

Thank you very much and best regards.

Hadi

My question deals with plotting a function, namely, x(t), from lower to higher values of t.

To this aim, I solved a simple differential equation with given initial conditions and then plotted for the result.

As it is seen, maple starts from lower values of t to higher ones. However, is there a command through which I can reverse the plotting procedure?  

From the attached file, "A question on plotting", we see that the slope of the curve at t=2 is positive when we observe it from "left to right". However, this slope is negative once we start plotting from "right to left".

Is there any command with which I can start plotting from right to left? or change of axis origin?

I would appreciate for your kind help and support.

My best regards

Hadi

 

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