Recently there has been a growing interest in designing efficient methods for the solution of ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin methods appear to be superior to other nonsampling methods and, in many cases, to several sampling methods. However, when the governing equations take complicated forms, numerical implementations of stochastic ...

We rigorously study a novel type of trigonometric Fourier collocation methods for solving multi-frequency oscillatory second-order ordinary differential equations (ODEs) q′′(t) + Mq(t) = f(q(t)) with a principal frequency matrix M ∈ Rd×d. If M is symmetric and positive semi-definite and f(q) = −∇U(q) for a smooth function U(q), then this is a multi-frequency oscillatory Hamiltonian system with ...

Collocation methods based on quartic splines are presented for second-order two-point boundary value problems. In order to obtain a uniquely solvable linear system for the degrees of freedom of the quartic spline collocation approximation, in addition to the boundary conditions specified by the problem, extra boundary or near-boundary conditions are introduced. Non-optimal (fourth-order) and op...

the importance and howness of language learning/ acquisition has been a great concern for decades. there are many factors that play important roles in this regard. this research compared the performance of native persian and english elementary students to see if there is any significant difference between the two groups and which type of collocation they performed better within the groups. for ...