View attachment 294303
Please help to solve this problem
View attachment 294304
Please advise to find the value of x to substitute
This question from City & Guilds Level 5 exam paperHi there,
I have to ask who gave you this problem to solve.
I ask because the numerical derivative equation in the drawing you provided is just first order (with the left f'(x)) and also it is for just a single variable.
To start, to solve a PDE like this you would need a second order, two variable numerical derivative. That's because both derivatives in the Laplace Equation are second order and depend on two variables, x and y. This means you will have two different formulas one for Uxx and another for Uyy. The only difference between the two is which variable gets incremented by 'h' and/or 'k' and which is taken as a constant. You could try to derive them yourself or i guess just look them up. If you try to derive them yourself i think you will get more insight out of this. You can start by deriving the second order central means formula for one variable, then go to the second order central means formula for two variables, and then you would also know how to move to three or more variables.
Luckily the Laplace Equation is static so it's easier to solve. This problem looks like it might be a potential problem where the field distribution is to be found, or at least a working formula for that.
It's been a while since i used the finite difference method in this fashion though so i'd have to look it up too. Most of the time in the past i would use the same numerical derivatives but i would plot the entire field so i can get an eye on the structure.
The Laplace Equation is pretty interesting and simpler because there is no time variable.
Did you know you could find an article on this right on this website if you do a search.
Hi,This question from City & Guilds Level 5 exam paper
The hand written equation in my post add by me because I have not familiar the equation , Now it is very clear that it needs two variable equation
I am still studding how to solve this problem
Can you please provide me a YouTube video that helps to solve this kind of problem . I searched but I could not found
Thank you so much for detailed explanation and advise
Please help to me if you have free time
Thanks again and again
This question from City & Guilds Level 5 exam paper
The hand written equation in my post add by me because I have not familiar the equation , Now it is very clear that it needs two variable equation
I am still studding how to solve this problem
Can you please provide me a YouTube video that helps to solve this kind of problem . I searched but I could not found
Thank you so much for detailed explanation and advise
Please help to me if you have free time
Thanks again and again
by Duane Benson
by Aaron Carman