"Nonlinear Differential Equations: Recent Developments in the Solution of Nonlinear Differential Equations" by B. Carpentier

This book collects research papers from leading world experts in the field, highlighting ongoing trends, progress, and open problems in this critically important area of mathematics.

Nonlinear differential equations are ubiquitous in computational science and engineering modeling, fluid dynamics, finance, and quantum mechanics, among other areas. Nowadays, solving challenging problems in an industrial setting requires a continuous interplay between the theory of such systems and the development and use of sophisticated computational methods that can guide and support the theoretical findings via practical computer simulations. Owing to the impressive development in computer technology and the introduction of fast numerical methods with reduced algorithmic and memory complexity, rigorous solutions in many applications have become possible.

Contents
1. Using the Boundary Element Method to Simulate Visco-Elastic Deformations of Rough Fractures
2. Asymptotic Behavior by Krasnoselskii Fixed Point Theorem for Nonlinear Neutral Differential Equations with Variable Delays
3. Spectral Properties of a Non-Self-Adjoint Differential Operator with Block-Triangular Operator Coefficients
4. Deformed Sine-Gordon Models, Solitons and Anomalous Charges
5. Continuous One Step Linear Multi-Step Hybrid Block Method for the Solution of First Order Linear and Nonlinear Initial Value Problem of Ordinary Differential Equations
6. Existence and Asymptotic Behaviors of Nonoscillatory Solutions of Third Order Time Scale Systems
7. Global Existence of Solutions to a Class of Reaction–Diffusion Systems on Rn
8. The Fourier Transform Method for Second-Order Integro-Dynamic Equations on Time Scales
9. Effect of Additive Perturbations on the Solution of Reflected Backward Stochastic Differential Equations
10. On Some Important Ordinary Differential Equations of Dynamic Economics
11. Multiple Solutions for Some Classes Integro-Dynamic Equations on Time Scales
12. Solution of Nonlinear Partial Differential Equations by Mixture Adomian Decomposition Method and Sumudu Transform
13. Positive Periodic Solutions for First-Order Difference Equations with Impulses
14. Peculiarities of the Fundamental Solution of Parabolic Systems with a Negative Genus
15. Boundary Element Modeling and Simulation Algorithm for Fractional Bio-Thermomechanical Problems of Anisotropic Soft Tissues
16. Solving Second-Order Differential Equations by Decomposition
17. The Uniformly Parabolic Equations of Higher Order with Discontinuous Data in Generalized Morrey Spaces and Elliptic Equations in Unbounded Domains
18. Gradient Optimal Control of the Bilinear Reaction–Diffusion Equation
19. Boundary Element Method for the Mixed BBM-KdV Equation Compared to Non Standard Boundary Conditions
20. On the Generalized Simplest Equations: Toward the Solution of Nonlinear Differential Equations with Variable Coefficients
21. Thermodynamic Stability Conditions as an Eigenvalues Fundamental Problem


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