Bessel and Modified Bessel ODEs Description Examples Description The general form of the Bessel ODE is given by the following: Bessel_ode := x^2*diff(y(x),x,x)+x*diff(y(x),x)+(x^2-n^2)*y(x); The general form of the modified Bessel ODE is given by the...
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 ...
functionhavebeen presented. Chapter twoLevinmethodfor ff(x)J=(rx)dx hasbeendiscussed andtheerror analyze andsomenumerical examples havebeenshowed, Chapter three twokinds ofmethodsto solve problem like f缸)厶(唧D))凼has beendiscussed.OneisLevin ...
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...
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...
(5) is an operator equation of the first kind which cannot be solved directly, since from Lemma 3, the trace operator AN is compact, and we do not know if the function f is in the range AN(ℂ2N+1) of AN. Therefore, we will solve the ill-posed operator equation (5) by a ...
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 ...
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. ...
Such inverse problems as the recovery of the potential from a Weyl function or the inverse two‐spectra Sturm–Liouville problem are its special cases. Moreover, the inverse problem of determining the shape of a human vocal tract also reduces to the considered inverse problem. The proposed ...