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Added adams-bashforth method of order 2, 3, 4, 5 #10969

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Merged
merged 9 commits into from
Oct 28, 2023
Merged

Added adams-bashforth method of order 2, 3, 4, 5 #10969

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3fa1efd
added runge kutta gills method
ravi-ivar-7 Oct 25, 2023
418693c
added adams-bashforth method of order 2, 3, 4, 5
ravi-ivar-7 Oct 25, 2023
548777c
[pre-commit.ci] auto fixes from pre-commit.com hooks
pre-commit-ci[bot] Oct 25, 2023
dc07518
Update adams_bashforth.py
ravi-ivar-7 Oct 25, 2023
45cb8ec
Deleted extraneous file, maths/numerical_analysis/runge_kutta_gills.py
ravi-ivar-7 Oct 26, 2023
a7283bc
Added doctests to each function adams_bashforth.py
ravi-ivar-7 Oct 28, 2023
c5a24b2
[pre-commit.ci] auto fixes from pre-commit.com hooks
pre-commit-ci[bot] Oct 28, 2023
729df6c
Update adams_bashforth.py
cclauss Oct 28, 2023
0703b9c
Update adams_bashforth.py
cclauss Oct 28, 2023
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Update adams_bashforth.py
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@cclauss
cclauss authored Oct 28, 2023
commit 0703b9ca40c0254f289f59cca269473b062f03e3
15 changes: 2 additions & 13 deletions maths/numerical_analysis/adams_bashforth.py
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Original file line number Diff line number Diff line change
@@ -1,7 +1,6 @@
"""
Use the Adams-Bashforth methods to solve Ordinary Differential Equations.


https://en.wikipedia.org/wiki/Linear_multistep_method
Author : Ravi Kumar
"""
Expand All @@ -25,20 +24,18 @@ class AdamsBashforth:

>>> def f(x, y):
... return x + y
>>> AdamsBashforth(f, [0, 0.2, 0.4], [0, 0.2, 1], 0.2, 1) # doctest: +ELLIPSIS
AdamsBashforth(func=..., x_initials=[0, 0.2, 0.4], y_initials=[0, 0.2, 1], step...)
>>> AdamsBashforth(f, [0, 0.2, 1], [0, 0, 0.04], 0.2, 1).step_2()
Traceback (most recent call last):
...
ValueError: The final value of x must be greater than the initial values of x.

>>> def f(x, y):
... return x + y
>>> AdamsBashforth(f, [0, 0.2, 0.3], [0, 0, 0.04], 0.2, 1).step_3()
Traceback (most recent call last):
...
ValueError: x-values must be equally spaced according to step size.

>>> def f(x, y):
... return x
>>> AdamsBashforth(f,[0,0.2,0.4,0.6,0.8],[0,0,0.04,0.128,0.307],-0.2,1).step_5()
Traceback (most recent call last):
...
Expand Down Expand Up @@ -73,8 +70,6 @@ def step_2(self) -> np.ndarray:
>>> AdamsBashforth(f, [0, 0.2], [0, 0], 0.2, 1).step_2()
array([0. , 0. , 0.06, 0.16, 0.3 , 0.48])

>>> def f(x, y):
... return (x -y)/2
>>> AdamsBashforth(f, [0, 0.2, 0.4], [0, 0, 0.04], 0.2, 1).step_2()
Traceback (most recent call last):
...
Expand Down Expand Up @@ -109,8 +104,6 @@ def step_3(self) -> np.ndarray:
>>> y[3]
0.15533333333333332

>>> def f(x, y):
... return (x -y)/2
>>> AdamsBashforth(f, [0, 0.2], [0, 0], 0.2, 1).step_3()
Traceback (most recent call last):
...
Expand Down Expand Up @@ -151,8 +144,6 @@ def step_4(self) -> np.ndarray:
>>> y[5]
0.5771083333333333

>>> def f(x, y):
... return (x -y)/2
>>> AdamsBashforth(f, [0, 0.2, 0.4], [0, 0, 0.04], 0.2, 1).step_4()
Traceback (most recent call last):
...
Expand Down Expand Up @@ -196,8 +187,6 @@ def step_5(self) -> np.ndarray:
>>> y[-1]
0.05436839444444452

>>> def f(x, y):
... return (x -y)/2
>>> AdamsBashforth(f, [0, 0.2, 0.4], [0, 0, 0.04], 0.2, 1).step_5()
Traceback (most recent call last):
...
Expand Down