If the particle can have an energy E < 0, it will be localized in and near the potential well, with a wave function that decays to zero as r increases to values greater than a. A simple case of this problem was one of our examples of an eigenvalue problem (Example 8.3.3), but ...
But, often a real nonlinear FDE has not the exact or analytical solution and must be solved numerically. Therefore, we aim to introduce a new numerical algorithm based on generalized Bessel function of the first kind (GBF), spectral methods and Newton–Krylov subspace method to solve nonlinear ...
efficientmethodstoevaluatethe quadratrue. Chapter oneboth the background and developments onthe quadratureofhighlyoscillatory functionhavebeen presented. Chapter twoLevinmethodfor ff(x)J=(rx)dx hasbeendiscussed andtheerror analyze andsomenumerical examples havebeenshowed, Chapter three twokinds ofmethodsto...
and used to compute the ARF function, which is the radiation force per unit characteristicenergy densityand surface cross-section of the spheroid. Numerical results are performed with particular emphasis on the waves’ amplitude ratio describing the evolution from progressive (traveling), quasi-standing...
(12) are exactly equivalent to considering \(p(v_{n,x},v_{n,y})\) as a delta function. We consider the reasonable assumption that the widths of the Gaussian distribution in the \(v_{2,x}\) and \(v_{2,y}\) directions are the same....
Using the continuity results, these transforms are extended as an adjoint to the corresponding dual space of distributions. The examples of Bessel wavelet transform of a polynomial function and a distribution are given. The Schrdinger equation is solved using the Bessel wavelet transform....
Also, an error problem is constructed by the residual function, and it is solved by the presented method. Thus, the error function is estimated, and the approximate solutions are improved. Finally, numerical examples are given to show the applicability of the method, and also, our results are...
In this paper, the linear differential difference equation subject to the mixed conditions has been solved numerically using Bessel polynomials. The solution is obtained in terms of Bessel polynomials. In addition, the accuracy and error analysis of the method are considered using residual function. ...
Correction of the approximated solution is obtained using the residual function of the operator equation. The error differential equation, gained by residual function, is solved by the Bessel collocation method (BCM). By summing the approximate solution of the error differential equation with the ...