Titlebook: Numerical Analysis and Its Applications; 5th International Co Ivan Dimov,István Faragó,Lubin Vulkov Conference proceedings 2013 Springer-Ve

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Flux-Splitting Schemes for Parabolic Problems time are constructed for parabolic equations without mixed derivatives. A peculiarity of the system of equations written in flux variables for equations with mixed derivatives is that there do exist coupled terms with time derivatives.

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Numerical Study of Maximum Norm a Posteriori Error Estimates for Singularly Perturbed Parabolic Probthe Crank-Nicolson method are considered. Certain critical details of the implementation are addressed. Based on numerical results we discuss various aspects of the error estimators in particular their effectiveness.

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Comparison Principle for Reaction-Diffusion-Advection Problems with Boundary and Internal Layersications as reaction-diffusion-advection equations. The theorems which state front motion description and stationary contrast structures formation are proved for parabolic, parabolic-periodic and integro-parabolic problems.

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Hybrid Functions for Nonlinear Differential Equations with Applications to Physical Problemsd Bernoulli polynomials are presented and are utilized to reduce the computation of nonlinear initial-value problems to a system of equations. The method is easy to implement and yields very accurate results.

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