I would like simulate alpha-T data of complex reaction for kinetic analysis, can anyone guide me how to solve this equation with RK4 method?Thanks
dy/dt=20*exp(-100000/(8.314*t))*(1-y1)^2+exp(-200000/(8.314*t))*(-ln(1-y2))^(0.5)
y0=0
y1,0=0
y2,0=0
y1+y2=2y
The problem looks interesting. To remove any possible confusion, can you provide a pdf or latex code of your equations? Also, check again if there is one more direct relation between y1 and y2
Also check if my understanding of your problem is correct, see attached picture. Since, logarithm of negative variable is undefined, 1-y2 must be greater than 0. This implies, y2 < 1. I assume that everything is in real domain!
Also, there should be additional constraints. Can y1 and y2 go negative Or, they have to be always greater than or equal to zero?
Also, recheck the powers of the terms (1-y1) and - ln (1-y2). You have mentioned 2 for the first term and 1/2 for the second. My intuition says they should be equal.
Do you want y values for any specific valuer of t? What is the desired domain of t for which the equation should be solved?
Give more information about the problem.
Hi,Vikash Pandey. Thanks for your answering. the domain of y1,y2 and y is:
0
Hi! Hosein,
Before we solve a given problem, dimensional consistency of the problem must be confirmed. This is where my doubt is.
You have the condition y1+ y2 = 2y. This implies y, y1 and y2 are of similar nature, that is, they have identical dimensions and units.
For eg. they can be concentration or any other relevant physical quantity in your case.
However, if you carefully observe the first and second term in the RHS of your differential equation, you will notice the two terms have addition "+" sign in between them. As I said earlier, this implies they both should have similar dimensions.
But the first term has (1-y1)^2 and second term has (- ln(1-y2))^0.5. This violates the dimensional consistency of the problem. You cannot add oranges and bananas together. :) The two terms should have same exponent (power) for the equation to be dimensionally consistent. They cannot have different power raised of 2 and 0.5.
So, please check it again!
Also check the picture I had attached earlier in my first post. Is the form of equation I have written correct?
Hi!
After reading the yellow highlighted section of the article you sent to me, I feel you have incorrectly written the question on researchgate post. Are you trying to obtain EXACTLY the same result as given in that article?
Hi.Vikash Pandey, Thanks for every thing,yes I want to obtain exactly the same result as given in that article, if possible, please send me your solving method,Thanks
Hi! I have recreated the plots of the article. Find details (codes and other useful information) in the attached zipped file.
Hi Vikash Pandey,
Can you guide me about neural network training for solid-state kinetic analysis that mentioned in below attached article and can help me, how to generate input data and what are the input and target matrix shapes for Ann? Thanks.
Well neural network is an integral part of machine learning/deep learning. It is also quite exhaustive. I suggest that first read/understand the topic from a standard book and only then jump to the research articles.
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