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:

---

Dependencies

R-3.3.2

Packages:

• ggplot2
• Deriv

---

Todo

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