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Volterra equation of the second kind in numerical methods

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Volterra equation

Volterra equation of the second kind

R language

Numeric solution by methods - finite sums and approximation


Parameters

Parameter Name Example
Free element of the equation FreeEl function(g) exp( - g )
Kernel Core function(g, s) exp( - ( g - s ) )
Count of steps in a grid step 100
Interval start point intstart 0
Interval end point intend 10
X-axis limits limits c(0.2, 0.5)
Quadrature for finite sums method "rectangle"
Method for calculation method_global "sum"
Error for approximation eps 0.05

Supported quadrature formulas for finite sums:

  1. Trapezoidal
  2. Parabolic (Simpson's rule)
  3. Rectangle (right)

Usage

Finite sums

f <- function(g) dnorm(g, 3, 0.5)
v <- volt(
	FreeEl = f, 
	Core = function(g, s) f(g-s), 
	step = 1000, 
	intend = 20, 
	method = "rectangle"
)
v$plot = v$plot + geom_hline(yintercept = 1/3, color = "red")
print(v$plot)

Approximation

f <- function(g) dnorm(g, 3, 0.5)
v <- volt(
    FreeEl = f, 
    Core = function(g, s) f(g-s), 
    step = 1000, 
    intend = 20, 
    method_global = "approx",
    eps = 0.07
)
v$plot = v$plot + geom_hline(yintercept = 1/3, color = "red")
print(v$plot)

Plot:

Plot Image


Dependencies

R-3.3.2

Packages:


Todo

  1. Fix error definition in finite sums
  2. Time tracker

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