maths.numerical_analysis.adams_bashforth

Use the Adams-Bashforth methods to solve Ordinary Differential Equations.

https://en.wikipedia.org/wiki/Linear_multistep_method Author : Ravi Kumar

Classes

AdamsBashforth

args:

Module Contents

class maths.numerical_analysis.adams_bashforth.AdamsBashforth

args: func: An ordinary differential equation (ODE) as function of x and y. x_initials: List containing initial required values of x. y_initials: List containing initial required values of y. step_size: The increment value of x. x_final: The final value of x.

Returns: Solution of y at each nodal point

>>> def f(x, y):
...     return x + y
>>> AdamsBashforth(f, [0, 0.2, 0.4], [0, 0.2, 1], 0.2, 1)  
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.

>>> 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.

>>> 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):
    ...
ValueError: Step size must be positive.

__post_init__() → None

step_2() → numpy.ndarray

>>> def f(x, y):
...     return x
>>> AdamsBashforth(f, [0, 0.2], [0, 0], 0.2, 1).step_2()
array([0.  , 0.  , 0.06, 0.16, 0.3 , 0.48])

>>> AdamsBashforth(f, [0, 0.2, 0.4], [0, 0, 0.04], 0.2, 1).step_2()
Traceback (most recent call last):
    ...
ValueError: Insufficient initial points information.

step_3() → numpy.ndarray

>>> def f(x, y):
...     return x + y
>>> y = AdamsBashforth(f, [0, 0.2, 0.4], [0, 0, 0.04], 0.2, 1).step_3()
>>> float(y[3])
0.15533333333333332

>>> AdamsBashforth(f, [0, 0.2], [0, 0], 0.2, 1).step_3()
Traceback (most recent call last):
    ...
ValueError: Insufficient initial points information.

step_4() → numpy.ndarray

>>> def f(x,y):
...     return x + y
>>> y = AdamsBashforth(
...    f, [0, 0.2, 0.4, 0.6], [0, 0, 0.04, 0.128], 0.2, 1).step_4()
>>> float(y[4])
0.30699999999999994
>>> float(y[5])
0.5771083333333333

>>> AdamsBashforth(f, [0, 0.2, 0.4], [0, 0, 0.04], 0.2, 1).step_4()
Traceback (most recent call last):
    ...
ValueError: Insufficient initial points information.

step_5() → numpy.ndarray

>>> def f(x,y):
...     return x + y
>>> y = AdamsBashforth(
...     f, [0, 0.2, 0.4, 0.6, 0.8], [0, 0.02140, 0.02140, 0.22211, 0.42536],
...     0.2, 1).step_5()
>>> float(y[-1])
0.05436839444444452

>>> AdamsBashforth(f, [0, 0.2, 0.4], [0, 0, 0.04], 0.2, 1).step_5()
Traceback (most recent call last):
    ...
ValueError: Insufficient initial points information.

func: collections.abc.Callable[[float, float], float]

step_size: float

x_final: float

x_initials: list[float]

y_initials: list[float]