Computing differential Galois groups of parameterized second-order linear differential equations

We develop algorithms to compute the differential Galois group G associated to a parameterized second-order homogeneous linear differential equation of the form

[EQUATION]

where the coefficients r₁, r₀ ∈ F(x) are rational functions in x with ...

Two-dimensional differential transform provides an effective tool to numerically solve partial differential equations. In this paper, we propose a general numerical solution of second-order linear partial differential equations using two-dimensional ...

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. ...