in this work the collocation method based on quartic b-spline is developed and applied to two-point boundary value problem in ordinary diferential equations. the error analysis and convergence of presented method is discussed. the method illustrated by two test examples which verify that the presented method is applicable and considerable accurate.

in this paper a mathematical simulation of a simplified internal combustion engine is presented. to contribute engine kinematics and its geometry, simple relations are derived for constrained motions. the equation of motion for the piston forms a singular boundary value problem. the uniqueness of the solution was studied in the banach space. for solving governing equations an iterative numerica...

krein [1] mentioned that for each pd equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary conditions. they claim it is not possible to have a related boundary value problem for an arbitrarily chosen operator in between. they have only considered lo...

Size-dependent longitudinal and torsional vibrations of nano-beams are examined by two-phase mixture integral elasticity. A new and efficient elastodynamic model is conceived by convexly combining the local phase with strain- and stress-driven purely nonlocal phases. The proposed stress-driven nonlocal integral mixture leads to well-posed structural problems for any value of the scale parameter...

This paper presents the bending analysis of annular plates by the indirect Trefftz boundary approach. The formulation for thin and thick plates is based on the Kirchhoff plate theory and the Reissner plate theory. The governing equations are therefore a fourth-order boundary value problem and a sixth-order boundary value problem, respectively. The Trefftz method employs the complete set of solu...

this paper presents the bending analysis of annular plates by the indirect trefftz boundary approach. the formulation for thin and thick plates is based on the kirchhoff plate theory and the reissner plate theory. the governing equations are therefore a fourth-order boundary value problem and a sixth-order boundary value problem, respectively. the trefftz method employs the complete set of solu...

‎In this paper‎, ‎we find matrix representation of a class of sixth order Sturm-Liouville problem (SLP) with separated‎, ‎self-adjoint boundary conditions and we show that such SLP have finite spectrum‎. ‎Also for a given matrix eigenvalue problem $HX=lambda VX$‎, ‎where $H$ is a block tridiagonal matrix and $V$ is a block diagonal matrix‎, ‎we find a sixth order boundary value problem of Atkin...

we investigate the boundary-value problem generated by the sturm-liouville equation withdiscontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditionsat the point of discontinuity. with a different approach we introduce an adequate hilbert spaceformulation, investigate some properties of eigenvalues, green’s function and resolvent operator, andfind simple c...

‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...