inteq 0.1.1

Solve various integral equations using the numerical methods of Betto and Thomas (2021).

Solve Volterra and Fredholm integral equations

This package estimates Volterra and Fredholm integral equations.

Volterra

This package provides the function SolveVolterra which approximates the solution, g(x), to the Volterra Integral Equation of the first kind:

using the method in Betto and Thomas (2021).

Parameters

k : function
    The kernel function that takes two arguments.
f : function
    The left hand side (free) function that takes one argument.
b : float
    Upper bound of the estimate, defaults to 1.
num : int
    Number of estimation points between zero and `b`.

Returns

grid : 2-D array
    Input values are in the first row and output values are in the second row.

Fredholm

This package provides the function SolveFredholm which approximates the solution, g(x), to the Fredholm Integral Equation of the first kind:

using the method described in Twomey (1963). It will return a smooth curve that is an approximate solution. However, it may not be a good approximate to the true solution.

Parameters

k : function
    The kernel function that takes two arguments.
f : function 
    The left hand side (free) function that takes one argument.
a : float
    Lower bound of the of the Fredholm definite integral, defaults to -1.
b : float
    Upper bound of the of the Fredholm definite integral, defaults to 1.
num : int
    Number of estimation points between zero and `b`.

Returns

grid : 2-D array
    Input values are in the first row and output values are in the second row.