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Abstract
We considerer parabolic partial differential equations: under the conditions , on a region . We will see that an approximate solution can be found using the techniques of generalized inverse moments problem and also bounds for the error of estimated solution. First we transform the parabolic partial differential equation to the integral equation . Using the inverse moments problem techniques we obtain an approximate solution of . Then we find a numerical approximation of when solving the integral equation , because solving the previous integral equation is equivalent to solving the equation .
Highlights
We considerer parabolic partial differential equation of the form: (1)M
Parabolic differential equations are commonly used in the fields of engineering and science for simulating physical processes
Parabolic partial differential equations have been numerically solved by using a variety of techniques [8] [9] [10] [11]
Summary
We considerer parabolic partial differential equation of the form:. M. Parabolic partial differential equations have been numerically solved by using a variety of techniques [8] [9] [10] [11]. In this paper we consider a different way to numerically solve the problem given by Equation (1) with conditions (2) and (3): we first transform it into an integral equation which we handle as a bidimensional moment problem. This approach was already suggested by Ang [25] in relation with the heat conduction equation.
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