Characterization of explosive volcanic eruptive processes from interpretation of deposits is a key for assessing volcanic hazard and risk, particularly for infrequent large explosive eruptions and those whose deposits are transient in the geological record. While eruption size-determined by measurement and interpretation of tephra fall deposits-is of particular importance, uncertainties for suc...

Abstract—In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of propose...

In this paper, we construct a numerical ‎method‎ to ‎the ‎solution ‎of‎ the Black-Scholes partial differential equation modeling the European option pricing problem with regard to a single asset‎. ‎W‎e use an explicit spline-difference scheme which is based on using a finite difference approximation for the temporal derivative and a cubic B-spline collocation for spatial derivatives. ‎The deriv...

In previous decades, many of the practical problems arising in scientific fields such as physics, engineering, and mathematics have been related to nonlinear fractional partial differential equations. One these equations, dissipative wave equation, has found a plethora useful applications different fields. A special class solutions studied for equation including exact approximate solutions. The...

Davis, P. J. Interpolation and approximation, Blaisdell New York 1969 Dikshit,H. P. and Rana, S. S. Cubic Interpolatory splines with non uniform Meshes J. Approx. Theory Vol 45, no4(1985) C. A. Hall and Meyer, W. W. ; Optimal error bounds for cubic spline Interpolation J. Approx. Theory, 58 (1989), 59-67. Kopotun K. A. : Univariate spline equivalence of moduli of smoothness and application . Ma...

Milk yield records (305d, 2X, actual milk yield) of 123,639 registered first lactation Holstein cows were used to compare linear regression (y = β(0) + β(1)X + e), quadratic regression, (y = β(0) + β(1)X + β(2)X(2) + e) cubic regression (y = β(0) + β(1)X + β(2)X(2) + β(3)X(3) +e) and fixed factor models, with cubic-spline interpolation models, for estimating the effects of inbreeding on milk yi...

Empirical Mode Decomposition (EMD) has been widely used to analyze non-stationary and nonlinear signal by decomposing data into a series of intrinsic mode functions (IMFs) and a trend function through sifting processes. For lack of a firm mathematical foundation, the implementation of EMD is still empirical and ad hoc. In this paper, we prove mathematically that EMD, as practiced now, only give...

A piecewise rational cubic spline [5] has been used to visualize the positive data in its natural form. The spline representation is interpolatory and applicable to the scalar valued data. The shape parameters in the description of a rational cubic have been constrained in such a way that they preserve the shape of the positive data in the view of positive curve. As far as visual smoothness is ...