Sumários

Module 2 - Lecture 7

12 dezembro 2017, 17:00 • Maria Teresa Romaozinho Marques Diogo

Details on

Collocation-type methods in discontinuous polynomial spline spaces.

Module 2- Lecture 6-

7 dezembro 2017, 16:00 • Maria Teresa Romaozinho Marques Diogo

A special  class of nonlinear singular VIES of Hammerstein-type.

Regularity results.
Low order numerical methods.
High order numerical methods (how to recover loss of optimal orders in case
of nonsmooth solutions)

Module 2- Lecture 5

23 novembro 2017, 16:00 • Maria Teresa Romaozinho Marques Diogo

.Numerical methods for Abel-type VIEs of the 2nd kind. The product Euler’s method and the product Trapezoidal method. Consistency and convergence; generalized discrete Gronwall inequality. Global order of convergence in the cases of smooth and non-differentiable solutions

Module 2- Lecture 4

21 novembro 2017, 17:00 • Maria Teresa Romaozinho Marques Diogo

Volterra integral equations with weakly singular kernels. Abel-type equation as a model in heat conduction problems; regularity properties of its solution. Unbounded (but integrable) kernels imply numerical methods based on product integration techniques. Examples.

Module 2- Lecture 3

16 novembro 2017, 16:00 • Maria Teresa Romaozinho Marques Diogo

Review of concepts of Interpolation theory and numerical integration.

  Numerical methods for 2nd kind Volterra integral equations with continuous kernels. Multistep methods based on Newton-Cotes quadrature rules. Consistency and convergence.