arXiv subjects

Ivan D. Gospodinov

Publications and source records attributed to Ivan D. Gospodinov.

3 recordsLinked to original sources

arXiv2017

Shooting-Projection Method for Two-Point Boundary Value Problems

This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of the differential equation is performed to obtain an initial value problem solution; then, the end value of the solution is used in a simple iteration formula to correct the initial condition; the process is repeated until the second boundary condition is satisfied. The iteration formula is derived utilizing an auxiliary function that satisfies both boundary conditions and minimizes the H1 semi-norm of the difference between itself and the initial value problem solution.

math.NA↗

arXiv2016

Constrained similarity of 2-D trajectories by minimizing the H1 semi-norm of the trajectory difference

This paper defines constrained functional similarity between 2-D trajectories via minimizing the H1 semi-norm of the difference between the trajectories. An exact general solution is obtained for the case wherein the components of the trajectories are mesh-functions defined on a uniform mesh and the imposed constraints are linear. Various examples are presented, one of which features application to mechanics and two-point boundary value problems. A MATLAB code is given for the solution of one of the examples. The code could easily be adjusted to other cases.

math.OC↗

arXiv2015

Meeting an absolute test information target with optimal number of test items via Grand Canonical Monte Carlo simulation

This work studies IRT-based Automated Test Assembly (ATA) of multiple test forms (tests) that meet an absolute target information function, i.e. selecting from an item bank only the tests that have information functions that are at a small distance away from the target. The authors introduce the quantities multiplicity of tests and probability of selecting a test with particular number of items N and distance E from the target. A Grand Canonical Monte Carlo test-assembly algorithm is proposed that selects tests according to this probability. The algorithm allows N to vary during the simulation. This work demonstrates that the number of tests that meet the target depends strongly on N. The algorithm is capable of finding tests with small values of E and various values of N depending on the need of the test constructor. Most importantly, it can determine the optimal N for which a maximal number of tests with certain specified small E exists.

math.NA↗