On the completely positive kernels for nonuniform meshes (Q6602247)

The following nonlinear Volterra integral equation of the second kind with convolutional kernel is considered:\N\[\Nu(t)=h(t)+\int\limits_{0}^{t}a(t-s)f(s,u(s))ds.\N\]\NThe complete positivity for convolutional kernels of such equations is discussed. The authors consider the complete positivity on uniform meshes and then explore the generalization of complete positivity to nonuniform meshes using the concept of pseudo-convolution. An illustrating example to see how this theory can be applied is also given.