Sturm-Liouville problems are abundant in the numerical treatment of scientific and engineering problems. In present contribution, we an efficient highly accurate method for computing eigenvalues singular boundary value The proposed uses double exponential formula coupled with sinc collocation method. This produces a symmetric positive-definite generalized eigenvalue system has convergence rate. Numerical examples presented comparisons single clearly illustrate advantage using formula.

We use the recently developed algorithm for $G_{n}^{(1)}$ transformation to approximate tail probabilities of normal distribution, gamma student's t-distribution, inverse Gaussian and Fisher's F distribution. Using this algorithm, which can be computed recursively when using symbolic programming languages, we are able compute these integrals high predetermined accuracies. Previous contribution, evaluation required computation large determinants. With our $G_n^{(1)}$ performed relatively...

We show that the double exponential sinc-collocation method provides an efficient uniformly accurate solution to one-dimensional time independent Schrödinger equation for a general class of rational potentials form V (x) = p(x)/q(x). The derived algorithm is based on discretization Hamiltonian using sinc expansions. This results in generalized eigenvalue problem, eigenvalues which correspond approximations energy values starting Hamiltonian. A systematic numerical study conducted, beginning...

Recently, we used the Sinc collocation method with double exponential transformation to compute eigenvalues for singular Sturm-Liouville problems. In this work, show that computation complexity of such a differential eigenvalue problem can be considerably reduced when its operator commutes parity operator. case, matrices resulting from are centrosymmetric. Utilizing well known properties centrosymmetric matrices, transform solving one large eigensystem into two smaller eigensystems. We only...

Sturm-Liouville problems are abundant in the numerical treatment of scientific and engineering problems. In present contribution, we an efficient highly accurate method for computing eigenvalues singular boundary value The proposed uses double exponential formula coupled with Sinc collocation method. This produces a symmetric positive-definite generalized eigenvalue system has convergence rate. Numerical examples presented comparisons single clearly illustrate advantage using formula.

In the present contribution, we apply double exponential Sinc-collocation method (DESCM) to one-dimensional time independent Schr\"odinger equation for a class of rational potentials form $V(x) =p(x)/q(x)$. This algorithm is based on discretization Hamiltonian using Sinc expansions. results in generalized eigenvalue problem where eigenvalues correspond approximations energy values corresponding Hamiltonian. A systematic numerical study conducted, beginning with test known and moving...

In this work, we propose a method combining the Sinc collocation with double exponential transformation for computing eigenvalues of anharmonic Coulombic potential. We introduce scaling factor that improves convergence speed and stability method. Further, apply to potentials leading highly efficient accurate computation eigenvalues.

A quantum anharmonic oscillator is defined by the Hamiltonian ${\cal H}= -\frac{ {\rm d^{2}}}{{\rm d}x^{2}} + V(x)$, where potential given $V(x) = \sum_{i=1}^{m} c_{i} x^{2i}$ with $c_{m}>0$. Using Sinc collocation method combined double exponential transformation, we develop a to efficiently compute highly accurate approximations of energy eigenvalues for oscillators. Convergence properties proposed are presented. principle minimal sensitivity, introduce an alternate expression mesh size...

The present contribution concerns the computation of energy eigenvalues a perturbed anharmonic coulombic potential with irregular singularities using combination Sinc collocation method and double exponential transformation. This provides highly efficient accurate algorithm to compute one-dimensional time-independent Schr\"odinger equation. numerical results obtained illustrate clearly efficiency accuracy proposed method. All our codes are written in Julia available on github at...