Journal ArticleDOI
Bounds for the solution of a second order differential equation with mixed boundary conditions
TLDR
In this article, a finite difference scheme is given for the numerical approximation of the real solution of the second order linear differential equation, lacking the first derivative, with mixed boundary conditions.Abstract:
A finite difference scheme is given for the numerical approximation of the real solution of the second order linear differential equation, lacking the first derivative, with mixed boundary conditions. The matrix associated with the resulting system of linear equations is tridiagonal and the overall discretization error isO (h4). The derived error bound is at most four times larger than the observed maximum error in absolute value for the numerical problem considered.read more
Citations
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Phase noise in coupled oscillators: theory and experiment
TL;DR: In this paper, the phase noise in mutually synchronized oscillator systems is analyzed for arbitrary coupling and injection-locking topologies, neglecting amplitude noise, and amplitude modulation to phase modulation (PM) conversion.
Journal ArticleDOI
The use of quartic splines in the numerical solution of a fourth-order boundary value problem
TL;DR: In this article, a uniform quartic polynomial spline function is derived via consistency relations connecting the quartic spline values at midknots and the corresponding values of the second and fourth derivatives, respectively.
Journal ArticleDOI
Parametric cubic spline solution of two point boundary value problems
TL;DR: This paper uses parametric cubic spline function to develop a numerical method, which is fourth order for a specific choice of the parameter, for computing smooth approximations to the solution for second order boundary value problems.
Journal ArticleDOI
Septic spline solutions of sixth-order boundary value problems
Shahid S. Siddiqi,Ghazala Akram +1 more
TL;DR: In this paper, the authors used septic spline for the numerical solution of the sixth-order linear, special case boundary value problem, and derived the end conditions for the definition of SE.
Journal ArticleDOI
Cubic spline method for solving two-point boundary-value problems
TL;DR: In this paper, uniform cubic spline polynomials are used to derive consistency relations and these relations are then used to develop a numerical method for computing smooth approximations to the solution and its first, second as well as third derivatives for a second order boundary value problem.
References
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Journal ArticleDOI
Properties of Some Tridiagonal Matrices and Their Application to Boundary Value Problems
Journal ArticleDOI
XVI.—Some Continuant Determinants arising in Physics and Chemistry—II
TL;DR: In this article, the authors considered the problem of determining the distribution of electric charge in crystals, metals, and large molecules in a regular lattice, each particle being acted upon by its nearest neighbours and perhaps by a fixed boundary.
Journal ArticleDOI
Bounds for the Solution of the Sturm-Liouville Problem with Application to Finite Difference Methods
A. K. Aziz,B. E. Hubbard +1 more
TL;DR: In this article, it was shown that the truncation error can be made arbitrarily small by making the mesh size h small, and that such an error bound may be obtained for certain finite difference analogues to a class of smooth problems.