Good book on integral equation? - Mathematics Stack Exchange
2012年2月29日 · I'm looking for a good reference on integral equations (i.e., an equation in which an unknown function appears under an integral sign such as the Fredholm equation). I would like something accessible but covers approaches to showing existence. Any …
Why are mathematician so interested to find theory for solving …
2014年3月19日 · Integral equations are often harder to solve by nature.. Every differential equation can be recast as an integral equation (or iterated integral equation) but the converse does not hold. Unfortunately, techniques for solving integral equations are somewhat few and far between with no real overarching paradigm.
Integral equations and the Fredholm alternative / theory
2018年10月12日 · (Note that $\lambda=0$ the integral equation is called Fredholm of the first kind, and $\lambda \neq 0$ is of second kind.) Adding to the confusion, some authors prefer to have $\lambda$ scaling the integral rather than $\phi(x)$ , in which case it makes sense to require it to be nonzero.
functional analysis - Relationship between integral equations and ...
$\begingroup$ Already integral equations are used in the proof of the existence and uniqueness theorem for ODE. For a book, DiBenedetto's 'Partial Differential Equations' has a discussion of integral equations (he treats somewhat explicitly the double layer potential method for the Laplacian). $\endgroup$ –
calculus - How to solve a system of integral equation
Putting $\displaystyle S(\lambda)=\sum_{j=0}^Na_j\lambda^j$ can the system of integral equations can be reduced to an algebraic equation? Thanks in advance. calculus
Volterra Equations of the First Kind - Mathematics Stack Exchange
2019年6月8日 · Recently, I managed to find a digital copy of "Handbook of Integral Equations" by Andrei D. Polyanin and Alexander V. Manzhirov (1998 edition). Linear integral equation of the first kind have the form:
Solving integral equation using Laplace transform
2014年6月29日 · Use of a Laplace Transform to solve Abel's Integral Equation Hot Network Questions "The Tiger's Paw" (Sangaku problem with six circles in an equilateral triangle, show that the ratio of radii is three to one.)
Solving an integral equation using the Fourier transform
I have to solve the equation $\int_0^{\infty} f(x) \cos{(\alpha x)}\, dx=\frac{\sin{\alpha }}{\alpha}$ Using fourier transform.
Resolvent Kernel of Volterra Integral Equation
Nevertheless, the analytic solution of the integral equation $\phi(x)=x+\lambda\int\limits_a^x\phi(s)ds$ is given below. Hoping this will help you to choose the right option. $$\frac{d\phi}{dx}=1+\lambda \phi(x)$$ The general solution of this linear ODE is : $$\phi(x)=-\frac{1}{\lambda}+c\:e^{\lambda x}$$ Bringing it back into the integral ...
Solving Volterra integral equation - Mathematics Stack Exchange
2016年5月15日 · I would like to solve $4u(t)+\int_0^t\sin(t-s)u(s)ds=5t, \ t\geqslant 0$. Any ideas on how to approach this equation?