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### 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) + ... + gn(x) hn(t)
• 16.1.3. Equations with Difference Kernel: K(x, t) = K(xt)
• 16.1.4. Reduction of Volterra Equations of the First Kind to Volterra Equations of the Second Kind
• 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) + ... + gn(x) hn(t)
• 16.2.3. Equations with Difference Kernel: K(x, t) = K(xt)
• 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
• 16.3. 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