In this paper we combine the method of fundamental solutions with various regularization
techniques to solve Cauchy problems of elliptic differential operators. The main idea is to …

In this paper, the Cauchy problem of inhomogeneous Helmholtz equation is investigated.
This problem is ill-posed and the truncation method is used to solve this inverse problem …

The Eulerian–Lagrangian method of fundamental solutions is proposed to solve the two-
dimensional unsteady Burgers' equations. Through the Eulerian–Lagrangian technique, the …

We investigate the continuation problem for the elliptic equation. The continuation problem
is formulated in operator form. The singular values of the operator A are presented and …

Numerical solution of ill‐posed boundary value problems normally requires iterative
procedures. In a typical solution, the ill‐posed problem is first converted to a well‐posed one …

This paper investigates the boundary particle method (BPM) coupled with truncated singular
value decomposition (TSVD) regularization technique on the solution of inverse Cauchy …

The Cauchy problem for the Helmholtz equation in an infinite “strip” is considered. The
Cauchy data are at the boundary x= 0 given in an approximate manner and the solution is …

This work deals with the Cauchy problem in two-dimensional linear elasticity. The equations
of the problem are discretized through a standard FEM approach and the resulting ill …

In this paper, we consider the Cauchy problem for the Helmholtz equation in a rectangle,
where the Cauchy data is given for y= 0 and boundary data are for x= 0 and x= π. The …

In this paper, the Cauchy problems for the Helmholtz equation are investigated. We propose
two regularization methods to solve them. Convergence estimates are presented under an a …