A numerical method for a class of non-linear integro-differential equations on the half line. (English) Zbl 1268.65163
Summary: We design and analyse a numerical method for the solution of the following second order integro-differential boundary value problem
\[
\nu (y)g(y)=\int_0^{\infty}k(x)g(x)dx(D(y)g'(y))'+p(y),~g'(0)=0,~\lim_{y\to +\infty} g(y)=0,
\]
which arises in the study of the kinetic theory of dusty plasmas. The method we propose represents a first insight into the numerical solution of more complicated problems and consists of a discretization of the differential and integral terms and of an iteration process to solve the resulting non-linear system. Under suitable hypotheses we prove the convergence. We will show the characteristics of the method by means of some numerical simulations.
Keywords:
boundary value problems; non-linear non-standard integro-differential equations; half-line; finite difference methods; quadrature; convergenceReferences:
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