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Researcher: Elliott, D (Professor David Elliott)

Fields of Research

Numerical analysis
Ordinary differential equations, difference equations and dynamical systems
Algebra and number theory
Numerical solution of differential and integral equations
Operator algebras and functional analysis
Mathematical aspects of classical mechanics, quantum mechanics and quantum information theory
Particle physics
Theoretical and applied mechanics
Other physical sciences
Approximation theory and asymptotic methods

Research Objectives

Expanding knowledge in the mathematical sciences
Expanding knowledge in the physical sciences

Career Best Publications

Research Publications

3 Algorithms for Hadamard finite-part integrals and fractional derivatives; Journal of Computational and Applied Mathematics
A complete error analysis for the evaluation of a two-dimensional nearly singular boundary element integral; Journal of Computational and Applied Mathematics
A generalisation of Telles' method for evaluating weakly singular boundary element integrals; Journal of Computational and Applied Mathematics
A new method for the numerical evaluation of nearly singular integrals on triangular elements in the 3D boundary element method; Journal of Computational and Applied Mathematics
A sinh tranformation for evaluating nearly singular boundary element integrals; International Journal for Numerical Methods in Engineering
A sinh transformation for evaluating two-dimensional nearly singular boundary element integrals; International Journal for Numerical Methods in Engineering
An algorithm for the approximate solution of integral equations of Mellin type; Numerische Mathematik
Clenshaw-Curtis and Gauss-Legendre quadrature for certain boundary element integrals; SIAM Journal on Scientific Computing
Dimensional renormalization in phi(3) theory: Ladders and rainbows; Physical Review D
Error analysis for a sinh transformation used in evaluating nearly singular boundary element integrals; Journal of Computational and Applied Mathematics
Error estimation of quadrature rules for evaluating singular integrals in boundary element problems; International Journal for Numerical Methods in Engineering
Estimates of the error in Gauss-Legendre quadrature for double integrals; Journal of Computational and Applied Mathematics
Gauss-Legendre quadrature for the evaluation of integrals involving the Hankel function; Journal of Computational and Applied Mathematics
Inverse momentum expectation values for hydrogenic systems; Journal of Mathematical Physics
On the approximate evaluation of Hadamard finite-part integrals; IMA Journal of Numerical Analysis
Sigmoidal transformations and the Euler-Maclaurin expansion for evaluating certain Hadamard finite-part integrals; Numerische Mathematik
Sigmoidal transformations and the trapezoidal rule; Journal of Australian Mathematical Society Series B Applied Mathematics
Sigmoidal-trapezoidal quadrature for ordinary and Cauchy principal value integrals; ANZIAM Journal
The compactness of a weakly singular integral operator on weighted Sobolev spaces; Journal of Integral Equations and Applications
The Cruciform Crack Problem and Sigmoidal Transformations; Mathematical Methods in Applied Sciences
The Euler-Maclaurin formula revisited; Journal of Australian Mathematical Society Series B Applied Mathematics
The finite Hilbert transform and weighted Sobolov spaces; Mathematische Nachrichten
The iterated sinh transformation; International Journal for Numerical Methods in Engineering
The method of steepest descent for estimating quadrature errors; Journal of Computational and Applied Mathematics
The Solution in a Class of Singular Functions of Cauchy Type Bisingular Integral Equations; Journal of Integral Equations and Applications
Transformations for evaluating singular boundary element integrals; Journal of Computational and Applied Mathematics
Using the iterated sinh transformation to evaluate two dimensional nearly singular boundary element integrals; Engineering Analysis with Boundary Elements

Research Projects

Approximation methods for singular integral equations; Australian Research Council (ARC)
Constructive methods for singular integral and integrodifferential equations; Australian Research Council (ARC)
Singular integral equations with shifts and complex conjugation; Australian Research Council (ARC)

Research Candidate Supervision

Numerical solutions of cauchy singular integral equations
Single Exponential Approximation of Fourier Transforms