A. D. Polyanin and A. V. Manzhirov, Handbook of Mathematics for Engineers and Scientists, Chapman & Hall/CRC Press, 2006 To book contents

16. Integral Equations

• 16.1. Linear Integral Equations of the First Kind with Variable Integration Limit
  • 16.1.1. Volterra Equations of the First Kind
  • 16.1.2. Equations with Degenerate Kernel: K(x, t) = g₁(x) h₁(t) + ... + g_n(x) h_n(t)
  • 16.1.3. Equations with Difference Kernel: K(x, t) = K(x − t)
  • 16.1.4. Reduction of Volterra Equations of the First Kind to Volterra Equations of the Second Kind
  • 16.1.5. Method of Quadratures
• 16.2. Linear Integral Equations of the Second Kind with Variable Integration Limit
  • 16.2.1. Volterra Equations of the Second Kind
  • 16.2.2. Equations with Degenerate Kernel: K(x, t) = g₁(x) h₁(t) + ... + g_n(x) h_n(t)
  • 16.2.3. Equations with Difference Kernel: K(x, t) = K(x − t)
  • 16.2.4. Construction of Solutions of Integral Equations with Special Right-Hand Side
  • 16.2.5. Method of Model Solutions
  • 16.2.6. Successive Approximation Method
  • 16.2.7. Method of Quadratures
• 16.3. Linear Integral Equations of the First Kind with Constant Limits of Integration
  • 16.3.1. Fredholm Integral Equations of the First Kind
  • 16.3.2. Method of Integral Transforms
  • 16.3.3. Regularization Methods
• 16.4. Linear Integral Equations of the Second Kind with Constant Limits of Integration
  • 16.4.1. Fredholm Integral Equations of the Second Kind. Resolvent
  • 16.4.2. Fredholm Equations of the Second Kind with Degenerate Kernel
  • 16.4.3. Solution as a Power Series in the Parameter. Method of Successive Approximations
  • 16.4.4. Fredholm Theorems and the Fredholm Alternative
  • 16.4.5. Fredholm Integral Equations of the Second Kind with Symmetric Kernel
  • 16.4.6. Methods of Integral Transforms
  • 16.4.7. Method of Approximating a Kernel by a Degenerate One
  • 16.4.8. Collocation Method
  • 16.4.9. Method of Least Squares
  • 16.4.10. Bubnov--Galerkin Method
  • 16.4.11. Quadrature Method
  • 16.4.12. Systems of Fredholm Integral Equations of the Second Kind
• 16.5. Nonlinear Integral Equations
  • 16.5.1. Nonlinear Volterra and Urysohn Integral Equations
  • 16.5.2. Nonlinear Volterra Integral Equations
  • 16.5.3. Equations with Constant Integration Limits
• References for Chapter 16

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