In this paper, we show that the conditional transform with respect to the Gaussian process involving the first variation can be expressed in terms of the conditional transform without the first variation. We then use this result to obtain various integration formulas involving the conditional $diamond$-product and the first variation.

In this paper we treat subjects which are relevant in the context of iterative methods in implicit time integration for compressible flow simulations. We present a novel renumbering technique, some strategies for choosing the time step in the implicit time integration, and a novel implementation of a matrix-free evaluation for matrix-vector products. For the linearized compressible Euler equati...

‎A numerical technique based on the collocation method using Legendre multiwavelets are‎ ‎presented for the solution of forced Duffing equation‎. ‎The operational matrix of integration for ‎Legendre multiwavelets is presented and is utilized to reduce the solution of Duffing equation‎ ‎to the solution of linear algebraic equations‎. ‎Illustrative examples are included to demonstrate‎ ‎the valid...

Organizations often encounter problems in the Product Integration process. The difficulties include finding errors at integration related to mismatch between the different components and problems in other parts of the system than the one that was changed. The question is if these problems can be decreased if the awareness of the integration process is increased in other activities. To get bette...

We reduce the two phase Stefan problem with kinetic to a system of nonlinear Volterra integral equations of second kind and apply Newton's method to linearize it. We found product integration solution of the linear form. Sufficient conditions for convergence of the numerical method are given and their applicability is illustrated with an example.

Online shopping is a very goal-oriented activity. Consumers have a set of preferences for a product or service that is used as criteria for assessment of the available alternatives. However, crucial information about products is often available as text reviews. Finding a product with specific features is extremely timeconsuming using the typical search functionality found in existing shopping s...