This paper presents a computational technique that called Tau-collocation method for the developed solution of non-linear integro-differential equations which involves a population model. To do this, the nonlinear integro-differential equations are transformed into a system of linear algebraic equations in matrix form without interpolation of non-poly-nomial terms of equations. Then, using coll...

We study the parametrized Hamiltonian action functional for finitedimensional families of Hamiltonians. We show that the linearized operator for the L2-gradient lines is Fredholm and surjective, for a generic choice of Hamiltonian and almost complex structure. We also establish the Fredholm property and transversality for generic S1-invariant families of Hamiltonians and almost complex structur...

In this paper, we present a Taylor-series expansion method for a class of Fredholm singular integro-differential equation with Cauchy kernel. This method uses the truncated Taylor-series polynomial of the unknown function and transforms the integro-differential equation into an nth order linear ordinary differential equa.tion with variable coefficients: ~y Galerkin method we use the orthogonal ...