00:01
We are given with the y dash is equals to e power y in 0 1 integral.
00:10
We have to solve it for runcotta method of fourth order.
00:14
Just writing in the derivative form it is y by dx is equals to e power y with y at 0 is equals to 1.
00:27
So runcotta method of fourth order predictor and mein -simpson method as corrector is y1 is equals to y0 plus 1 by 6 into k1 plus 2 times k2 plus 2 times k3 plus k4 which is the formula.
00:54
We have to find this y1.
00:56
Here h is equals to 0.
00:59
So formula for k1 is h f of x0 y0.
01:09
What is f here? our f is e power y.
01:14
Put the values here.
01:16
H is 0 .2.
01:19
So h is 0 .2.
01:21
Put the value f at x0 and y0.
01:25
X0 is 0 and y0 is 1.
01:28
We will get e power 1.
01:31
So k1 we have find.
01:33
Put e power 1 value.
01:35
We will get 0 .5437.
01:41
Now we will find k2.
01:46
K2 is equals to h into f of x0 plus h by 2 into comma y0 plus k1 over 2.
02:02
Here is a not h and here is a k1.
02:04
Now k2 is equals to put the value of h which is 0 .2.
02:09
Now we have to put the value function x is x0 plus h by 2 and y0 is y0 plus k by 2.
02:19
We will get f x0 is 0 and h is 0 .2.
02:24
0 .2 by 2 is 0 .1 comma.
02:29
Y0 was 1.
02:31
So 1 plus k1.
02:32
K1 we have find here and divide it by 2 and with 1.
02:36
We will get 1 .2718.
02:43
Put these value in the f.
02:46
We get 0 .2 into e power 1 .2718.
02:54
Put its value and multiply it with 0 .2.
02:58
We will get 0 .7134.
03:05
We find the value of k2...