The transmutation operator method is extended to the case of functions two variables. flattens function, i.e. replaces a function with discontinuous partial derivatives on coordinate axes by continuously differentiable function. work reveal properties operator, and prove commutativity Laplace operator. It was found that Cauchy problem for equation internal conjugations in an unbounded domain ca...

We develop and apply the product integration method to a large class of linear weakly singular Volterra systems. We show that under certain sufficient conditions this method converges. Numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

we develop and apply the product integration method to a large class of linear weakly singular volterra systems. we show that under certain sufficient conditions this method converges. numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

This paper deals with transient non-linear heat conduction through the insulation wall of the tank for transportation of liquid aluminum. Tanks designed for this purpose must satisfy certain requirements regarding temperature of loading and unloading, during transport. Basic theoretical equations are presented, which describe the problem of heat conduction finite element analysis, starting from...