Volterra Integral Equation of the First Kind

An Integral Equation of the form

$$\phi(x) = \int^x_a k(x,t)\phi (t)\,dt.$$

See also Fredholm Integral Equation of the First Kind, Fredholm Integral Equation of the Second Kind, Integral Equation, Volterra Integral Equation of the Second Kind

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 865, 1985.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Volterra Equations.'' §18.2 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 786-788, 1992.