Fast algorithms for interpolation with L-splines for differential operators <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e202" altimg="si459.svg"><mml:mi>L</mml:mi></mml:math> of order 4 with constant coefficients

Study on usage of Elzaki transform for the ordinary differential equations with non-constant ‎coefficients

Although Elzaki transform is stronger than Sumudu and Laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. In this paper, a method is introduced to find that a differential equation by Elzaki transform can be ‎solved?‎

Piecewise L-splines of order 4: Interpolation and L2 error bounds for splines in tension

Piecewise L-splines are generalizations of L-splines, in the sense that they satisfy different differential equations in different mesh intervals. Prenter attempted in [P.M. Prenter, Piecewise L-Splines, Numer. Math. 18 (2) (1971) 243–253] to obtain results on piecewise L-splines by generalizing the results of Schultz and Varga on L-splines in [M.H. Schultz, R.S. Varga, L-Splines, Numer. Math. ...

Splines: on scale, differential operators and fast algorithms

Images of Commuting Differential Operators of Order One with Constant Leading Coefficients

We first study some properties of images of commuting differential operators of polynomial algebras of order one with constant leading coefficients. We then propose what we call the image conjecture on these differential operators and show that the Jacobian conjecture [BCW], [E] (hence also the Dixmier conjecture [D]) and the vanishing conjecture [Z3] of differential operators with constant coe...

The spectrum of differential operators of order 2n with almost constant coefficients

We discuss the spectral properties of higher order ordinary differential operators. If the coefficients differ from constants by small perturbations, then the spectral properties are preserved. In this context, “small perturbations” are either short range (i.e., integrable) or long range, but slowly varying. This generalizes classical results on second order operators. Our approach relies on an...