Articles

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Numerical experiments with model equations of cancer invasion of tissue (with Mikhail Kolev), Control and Cybernetics (2011)

In this paper we investigate a mathematical model of cancer invasion of tissue, which incorporates...

 

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Numerical Versus Experimental Data for Prostate Tumour Growth (with Mikhail Kolev), Journal of Biological Systems (2011)

The goal of this paper is to solve mathematical model equations on solid tumour growth...

 

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Numerical Solutions for a Model of Tissue Invasion and Migration of Tumour Cells (with Mikhail Kolev), Computational and Mathematical Methods in Medicine (2011)

The goal of this paper is to construct a new algorithm for the numerical simulations...

 

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Nonlinear Modeling with Mammographic Evidence of Carcinoma (with K. Drucis, M. Kolev, and W. Majda), Nonlinear Analysis: Real World Applications (2010)

The goal of this paper is to apply oncological data for mathematical modeling of breast...

 

Numerical Solution of a Model for Brain Cancer Progression After Therapy (with Z. Jackiewicz, Y. Kuang, and C. Thalhauser), Mathematical Modelling and Analysis (2009)

We present a numerical scheme used to investigate a mathematical model of tumor growth which...

 

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Finite-Difference and Pseudo-Sprectral Methods for the Numerical Simulations of In Vitro Human Tumor Cell Population Kinetics (with Z. Jackiewicz and B. Basse), Mathematical Biosciences and Engineering (2009)

Pseudo-spectral approximations are constructed for the model equations which describe the population kinetics of human...

 

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Correlation Between Animal and Mathematical Models for Prostate Cancer Progression (with Z. Jackiewiczy, Cheryl L. Jorcyk, and M. Kolevx), Computational & Mathematical Methods in Medicine (2009)

This work demonstrates that prostate tumour progression in vivo can be analysed by using solutions...

 

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Discrete Variable Methods for Delay-Differential Equations with Threshold-Type Delays (with Z. Jackiewicz), Journal of Computational and Applied Mathematics (2009)

We study numerical solution of systems of delay-differential equations in which the delay function, which...

 

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Delay partial diļ¬€erential equations, Scholarpedia (2008)

A delay partial differential equation (DPDE) is an equation which involves: (1) at least two...

 

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Numerical solution of Volterra integro-differential equations modeling thalamo-cortical systems (with F.C. Hoppensteadt and Z Jackiewicz), PAMM Wiley Interscience Journal, Proc. Appl. Math. Mech (2008)
 

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A variant of pseudospectral method for activity-dependent dendritic branch model (with M. Dur-e-ahmad, S. Crook, and Z. Jackiewicz), J. of Neuroscience Methods (2007)
 

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Numerical solution of Volterra integral and integro-differential equations with rapidly vanishing convolution kernels (with F.C. Hoppensteadt and Z. Jackiewicz), BIT Numerical Mathematics (2007)
 

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Numerical solutions of thalamo-cortical systems (with Z. Jackiewicz), Numerical analysis and approximation theory (2006)
 

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Spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations (with Z. Jackiewicz), Appl. Numer. Math. (2006)
 

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An Iterated Pseudospectral Method for Functional Partial Differential Equations (with Jodi Mead), Applied Numerical Mathematics (2005)

Chebyshev pseudospectral spatial discretization preconditioned by the Kosloff and Tal-Ezer transformation [10] is applied to...

 

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Spectral collocation and waveform relaxation methods with Gengenbauer reconstruction for nonlinear conservation laws (with Z Jackiewicz), Comput. Methods Appl. Math. (2005)
 

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The stability of numerical approximations of the time domain current induced on a thin wire and strip antennas (with P. J. Davies and D. B. Duncan), Appl. Numer. Math. (2005)
 

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Error bounds for spatial discretization and waveform relaxation applied to parabolic functional-differential equations, J. Math. Anal. Appl. (2004)
 

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Fourier stability analysis of a numerical method for time domain electromagnetic scattering from a thin wire (with P. J. Davies), Numer. Algorithms (2004)
 

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On the stability of Radau IIA collocation methods for delay differential equations (with K. in 't Hout), Math. Comput. Modelling (2004)
 

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Spectral versus pseudospectral solutions of the wave equation by waveform relaxation methods (with Z. Jackiewicz and B.D. Welfert), J. Sci. Comput. (2004)
 

Contributions to Books

Numerical Experiments For Mammary Adenocarcinoma Cell Progression (with Cheryl Jorcyk and Mikhail Kolev), Integral Methods in Science and Engineering, Computational and Analytic Aspects (2011)

An estimated 192,370 women in the United States were diagnosed with breast cancer during 2009....

 

Numerical solution of Volterra integro-differential equations modeling thalamo-cortical systems (with Frank C. Hoppensteadt and Zdzislaw Jackiewicz), PAMM Wiley (2008)

Our study concerns thalamo-cortical systems which are modelled by nonlinear systems of Volterra integro-differential equa-...

 

Numerical solutions of thalamo-cortical systems (with Zdzislaw Jackiewicz), Numerical Analysis and Approximation Theory (2006)

Thalamocortical problems, which are written as systems of Volterra integro-differential equations, are studied. Waveform relaxation,...

 

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Pseudospectral Iterated Method for Differential Equations with Delay Terms (with Jodi Mead), Lecture Notes in Computer Science (2004)

New efficient numerical methods for hyperbolic and parabolic partial differential equations with delay terms are...

 

Convergence of the method of lines for parabolic differential-functional equations, Advances in difference equations (1997)

Parabolic differential-functional equations with initial-boundary conditions of the Dirichlet type are studied. Spatial derivatives occurring...