This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by an additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave fi...

‎in this paper‎, ‎a numerical procedure for an inverse problem of‎ ‎simultaneously determining an unknown coefficient in a semilinear ‎parabolic equation subject to the specification of the solution at‎ ‎an internal point along with the usual initial boundary conditions ‎is considered‎. ‎the method consists of expanding the required‎ ‎approximate solution as the elements of the inverse quadrati...

in this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear volterra integral equations of the first-kind is proposed. this problem is transformedto a nonlinear two-dimensional volterra integral equation of the second-kind. the properties ofthe bivariate shifted legendre functions are presented. the operational matrices of integrationtogether with the produ...

In this paper, a numerical solution of an inverse non-dimensional heat conduction problem by spline method will be considered. The given heat conduction equation, the boundary condition, and the initial condition are presented in a dimensionless form. A set of temperature measurements at a single sensor location inside the heat conduction body is required. The result show that the proposed meth...