This collection covers new aspects of numerical methods in applied mathematics, engineering, and health sciences. It provides recent theoretical developments and new techniques based on optimization theory, partial differential equations (PDEs), mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena. Specific topics covered in detail include new numerical methods for nonlinear partial differential equations, global optimization, unconstrained optimization, detection of HIV- Protease, modelling with new fractional operators, analysis of biological models, and stochastic modelling.
Chapter
1. Monotone iterative technique for non-autonomous semilinear
differential equations with non-instantaneous impulses.
Chapter
2. An
extrapolated Crank Nicholson VMS-POD method for Darcy Brinkman Equations.-
Chapter
3. Comparison of Exact and Numerical Solutions for the
Sharma-Tasso-Olver Equation.
Chapter
4. A Linear Bspline Approximation for
a Class of Nonlinear Time and Space Fractional Partial Differential
Equations.
Chapter
5. Escaping from Current Minimizer by Using an Auxiliary
Function Smoothed by Bezier Curves.
Chapter
6. A modified Laguerre matrix
approach for Burger-Fisher type nonlinear equations.
Chapter
7. Increasing
the Effects of Auxiliary Function by Multiple Extrema in Global
Optimization.
Chapter
8. A New Approach for the Solution of the Generalized
Abel Integral Equation.
Chapter
9. NPSOG: A new hybrid method for
unconstrained differentiable optimization.
Chapter
10. Detection of HIV-1
Protease Cleavage Sites via Hidden Markov Model and Physiochemical Properties
of Aminoacids.
Chapter
11. A Numerical Approach for Variable Order
Fractional Equations.
Chapter
12. Evolution of Plane Curves via Lie Symmetry
Analysis in the Galilean Plane.
Jose A. Tenreiro Machado is a Professor at the Institute of Engineering, Polytechnic of Porto, Portugal; Necati Özdemir is a Professor with the Department of Mathematics, Balkesir University, Balkesir, Turkey; Dumitru Baleanu is a Professor with the Department of Mathematics, Ēankaya University, Ankara, Turkey and the Institute of Space Sciences, Magurele-Bucharest, Romania.
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