Can you help me? it's about numerical numbers question.
i want to fourth derivative like this first derivative solution.
And with analytical solution.
Transcribed Image Text:First Derivative
Error
f'(x)% =
O(h)
2h
-f(x)+ 8f(x)-8f(x) + f(x,-2)
f (x) =
12h
Second Derivative
f(x)-2f(x) +f(x-)
f"(x) =
-f(K) + 16f(x,)- 30ƒ(x) + 16ƒ(x,-1) – f(x,-)
12
f"(x) =-
O(k")
Third Derivative
f(x,,2) – 2f(x,) + 2f(x_;) – f(x__2)
f" (x,) =
O(h)
2h
-f(x,) + 8ƒ(x,,2) - 13f(x,,) + 13f(x,-1) – 8ƒ(x, 2) + f(x,)
8h
f"(x) =
Fourth Derivative
f(x)-4f(x,)+6f(x) – 4f(x,-1) + f(x}-2)
f"(x) =
-f) + 12f(x,,) + 39ƒ(x,,) + 56ƒ(x) – 39f(x_.,) + 12fK,--) + f(x_)
f"(x) =
In the above table, the formulations to calculate different order derivatives of a function are given by using the
çentral difference method.
For the function f (x) = In (x), obtain the first, second, third and fourth order derivatives of this function by using
the above methods for the neighborhood step h = 0.01 at the point x = 4.0.
Soru çözüm formatı oluşturması adına birinci türevin elde edilme yöntemi aşağıda verilmiştir
f(x) =In (x) ƒ (4.0) = ? ƒ "(4.0)=? f"(4.0)=? ƒ ""(4.0) = ?
h= 0.01 için x, = 4.00 x- = 4.01 x- = 3.99 x,2 = 4.02 x-2 = 3.98
İki nokta için birinci türev
f (4.01)–f (3.99) 1.3888 –1.3838
= 0.25
f'(4.0) =
2(0.01)
0.02
Dört nokta için birinci türev
-f (4.02)+8ƒ(4.01) – 8ƒ (3.99)+ f (3.98) (-1.3913)+8(1.3888) – 8(1.3838)+1.3813
f'(4.0) =
= 0.25
12 (0.01)
12(0.01)
Analitik çözüm
f (x) = In (x) → ƒ(x)=1/x → f'(4.0)= 0.25
Using the solution format given above, obtain the second, third and fourth order derivatives of the
function f (x) = In (x). Compare the results you get with the numerical solution with the derivatives
you get with the analytical solution for the relevant function.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.