Hi,
I want to solve trwo consecutive differential equations in Mathcad 15, which is like following picture,
Actually, I want to get the plot of S(r) with r. In addition, "r" ranges from 0 to 0.001. I don't know how to deal with my error, hope to get your help.
Please, kindly find the attachment about this task. Thank you very much.
Jason
ACCEPTED SOLUTION
Accepted Solutions
Mathcad's Quickplot isn't perfect.
Either use a range variable for r
or at least set the start and end point for the plot manually:
I'd say rather than too few initial conditions, you have too many (namely 4 instead of 2).
First of all let's establish that you have a single differential equation for the function W(r). That is because S(r) is NOT involved in the first equation.
The second equation tells that W(r) is the derivative of S(r) multiplied with a constant.
So you only have to solve the first differential equation to find W(r) and then S(r) can be found by integrating.
You might indeed say they're consecutive: one follows the other. They're not simultaneous!
Let's do some work:
I would guess that this solution implicitly assumes that W(0)=0 and S(0)=0, which is pretty close to two of the initial conditions you've provided.
You say that r ranges from 0 to 0.001. Well here's the plot:
Does this meet your expectations?
Luc
Here is a third approach, following more closely what you had tried to do:
1) You have two functions W and S - so you have to solve for both, not just for S
2) You had a typo in the last W(r). You had a multiplication W*(r)
3) You cannot chose r=0 as start value -> division by zero (first equation, if solved for the derivation of W).
4) Its was already said: you had too much initial conditions for a system of just two DE's of 1st order
Regards, Werner
Thank you for your detail solution. It's very useful for me. And, I 'm sorry I give the wrong first equation, the right equation is as following:
As you can see from the above picture, I still can't get the plot. I don't know why?
In addition, I have know the condition from question, S(0.001)=0.0001, which is not matched with your plot. Could you help me figure out what's wrong?
Please kindly find the attachment.
Best wishes,
Jason
Mathcad's Quickplot isn't perfect.
Either use a range variable for r
or at least set the start and end point for the plot manually:
