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- Lars Eldén, Fredrik Berntsson, Teresa Reginska
- SIAM J. Scientific Computing
- 2000

We consider an inverse heat conduction problem, the Sideways Heat Equation, which is a model of a problem, where one wants to determine the temperature on both sides of a thick wall, but where one side is inaccessible to measurements. Mathematically it is formulated as a Cauchy problem for the heat equation in a quarter plane, with data given along the line… (More)

Fredrik Berntsson, Vladimir Kozlov, Lydie Mpinganzima and Bengt-Ove Turesson, An alternating iterative procedure for the Cauchy problem for the Helmholtz equation, 2014, Inverse Problems in Science and Engineering, (22), 1, 45-62. Inverse Problems in Science and Engineering is available online at informaworldTM:… (More)

- Emanuel Evarest, Fredrik Berntsson, Martin Singull, Wilson Charles
- 2016

Two regime switching models for predicting temperature dynamics are presented in this study for the purpose to be used for weather derivatives pricing. One is an existing model in the literature (Elias model) and the other is presented in this paper. The new model we propose in this study has a mean reverting heteroskedastic process in the base regime and a… (More)

We consider an inverse heat conduction problem, the sideways heat equation, which is the model of a problem where one wants to determine the temperature on the surface of a body, using internal measurements. Mathematically it can be formulated as a Cauchy problem for the heat equation, where the data is given along the line x = 1, and a solution is sought… (More)

- Fredrik Berntsson, Matts Karlsson, Vladimir A. Kozlov, Serguei A. Nazarov
- Applied Mathematics and Computation
- 2016

In this paper we present a one-dimensional model of blood flow in a vessel segment with an elastic wall consisting of several anisotropic layers. The model involves two variables: the radial displacement of the vessel’s wall and the pressure, and consists of two coupled equations of parabolic and hyperbolic type. Numerical simulations on a straight segment… (More)

The thermal conductivity properties of a material can be determined experimentally by using temperature measurements taken at specified locations inside the material. We examine a situation where the properties of a (previously known) material changed locally. Mathematically we aim to find the coefficient k(x) in the stationary heat equation (kTx)x = 0;… (More)

∆u+ ku = 0 in Ω, u = f on Γ0, ∂νu = g on Γ0, where k is the wave number, ∂ν denotes the outward normal derivative, and f and g are specified Cauchy data on Γ0. This problem is ill–posed. In [3], we developed a modification of the alterating iterative algorithm that we used to solve this problem. This modification is based on the alternating iterative… (More)

- Fredrik Berntsson, Lars Eld
- 2007

We consider a two dimensional steady state heat conduction problem. The Laplace equation is valid in a domain with a hole. Temperature and heat{{ux data are speciied on the outer boundary, and we want to compute the temperature on the inner boundary. This Cauchy problem is ill{posed, i.e. the solution does not depend continuously on the boundary data, and… (More)

The sideways heat equation is a one dimensional model of a problem, where one wants to determine the temperature on the surface of a body using interior measurements. More precisely, we consider a heat conduction problem, where temperature and heat–flux data are available along the line x=1 and the solution is sought in the interval 0≤x <1. The problem is… (More)

- Emanuel Evarest, Fredrik Berntsson, Martin Singull, Xiangfeng Yang
- 2017

In this study we discuss the pricing of weather derivatives whose underlying weather variable is temperature. The dynamics of temperature in this study follows a two state regime switching model with a heteroskedastic mean reverting process as the base regime and a shifted regime defined by Brownian motion with mean different from zero. We develop the… (More)