Philippe Gaudreau

The double exponential sinc collocation method for singular Sturm-Liouville problems

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

Computation of Tail Probabilities via Extrapolation Methods and Connection with Rational and Padé Approximants

We use the recently developed algorithm for the

Improvements to the cluster Newton method for underdetermined inverse problems

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On the Computation of Eigenvalues of the Anharmonic Coulombic Potential

transformation to approximate tail probabilities of the normal distribution, the gamma distribution, the students

Double exponential sinc-collocation method for solving the energy eigenvalues of harmonic oscillators perturbed by a rational function

t

Refuge-mediated predator-prey dynamics and biomass pyramids

-distribution, the inverse Gaussian distribution, and Fishers

Computing Energy Eigenvalues of Anharmonic Oscillators using the Double Exponential Sinc collocation Method

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An asymptotic expansion for energy eigenvalues of anharmonic oscillators

distribution. Using this algorithm, which can be computed recursively when using symbolic programming languages, we are able to compute these integrals to high predetermined accuracies. Previous to this contribution, the evaluation of these tail probabilities using the

Computation of tail probability distributions via extrapolation methods and connection with rational and Padé approximants.

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Centrosymmetric Matrices in the Sinc Collocation Method for Sturm-Liouville Problems

transformation required symbolic computation of large determinants. With the use of our algorithm, the