Homotopy Analysis Method in Nonlinear Differential Equations

Part I. Basic Ideas and Theorems

1. Introduction
Shijun Liao

2. Basic Ideas of the Homotopy Analysis Method
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3. Optimal Homotopy Analysis Method
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4. Systematic Descriptions and Related Theorems
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5. Relationship to Euler Transform
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6. Some Methods Based on the HAM
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Part II. Mathematica Package BVPh and Its Applications

7. Mathematica Package BVPh
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8. Nonlinear Boundary-value Problems with Multiple Solutions
Shijun Liao

9. Nonlinear Eigenvalue Equations with Varying Coefficients
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10. A Boundary-layer Flow with an Infinite Number of Solutions
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11. Non-similarity Boundary-layer Flows
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12. Unsteady Boundary-layer Flows
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Part III. Applications in Nonlinear Partial Differential Equations

13. Applications in Finance: American Put Options
Shijun Liao

14. Two and Three Dimensional Gelfand Equation
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15. Interaction of Nonlinear Water Wave and Nonuniform Currents
Shijun Liao

16. Resonance of Arbitrary Number of Periodic Traveling Water Waves
Shijun Liao

Avainsanat: Mathematics, Partial Differential Equations, Nonlinear Dynamics, Appl.Mathematics/Computational Methods of Engineering, Ordinary Differential Equations