In this paper, a Chebyshev finite difference method has been proposed in order to solve nonlinear two-point boundary value problems for second order nonlinear differential equations. A problem arising from chemical reactor theory is then considered. The approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference schem...

Differential-algebraic equations with higher index give rise to essentially ill-posed problems. Therefore, their numerical approximation requires special care. In the present paper, we state the notion of ill-posedness for linear differential-algebraic equations more precisely. Based on this property, we construct a regularization procedure using a least-squares collocation approach by discreti...

in this paper, an effective direct method to determine the numerical solution of linear and nonlinear fredholm and volterra integral and integro-differential equations is proposed. the method is based on expanding the required approximate solution as the elements of chebyshev cardinal functions. the operational matrices for the integration and product of the chebyshev cardinal functions are des...

Linear, possibly overor underdetermined, differential-algebraic equations are studied that have the same solution behavior as linear differential-algebraic equations with well-defined strangeness index. In particular, three different characterizations are given for differential-algebraic equations, namely by means of solution spaces, canonical forms, and derivative arrays. Two levels of general...

In this paper we apply the idea of Dixon resultant to algebraic differential equations and introduce the Dixon differential resultant. We prove that a necessary condition for the existence of a common solution of two algebraic differential equations is that the differential resultant is equal to zero, which actually provides a method of elimination and reduces a system of multi-variate differen...

Numerical methods for design sensitivity analysis of multibody dynamics are presented. An analysis of the index-3 adjoint differential-algebraic equations is conducted and stability of the integration of the adjoint differential-algebraic equations in the backward direction is proven. Stabilized index-1 formulations are presented and convergence of backward differentiation formulas is shown for...

Linear, possibly overor underdetermined, differential-algebraic equations are studied that have the same solution behavior as linear differential-algebraic equations with well-defined strangeness index. In particular, three different characterizations are given for differential-algebraic equations, namely by means of solution spaces, canonical forms, and derivative arrays. Two levels of general...

In this study, the vibration of cracked plates is investigated using the differential quadrature method and experimental modal analysis. The crack, which is assumed to be open, is modeled by the extended rotational spring. With its finite length, the crack divides the plate into six segments. Then, the differential quadrature is applied to the governing differential equations of motion and the ...

the partial differential equations for water flow and solute transport in a two-dimensional saturated domain are rendered discrete using the finite difference technique; the resulting system of algebraic equations is solved using a dynamic programming (dp) method. the advantage of the dp algorithm is that the problem is converted from solving an algebraic system of order nc(nl-1) nc(nl-1) into...

High index differential algebraic equations (DAEs) are ordinary differential equations (ODEs) with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields. In this paper, we generalize the idea of differential elimination with Dixon resultant to polynomially nonlinear DAEs. We propose a new algorithm for index reduction of DAEs and establish...