Bernstein Series Solution of the Heat Equation in 2-D

Parallel Numerical Solution of 2-D Heat Equation

In this paper, we will discuss the numerical solution of the two dimensional Heat Equation. An approximation to the solution function is calculated at discrete spatial mesh points, proceeding in discrete time steps. The starting values are given by an initial value condition. We will first explain how to transform the differential equation into a finite difference equation, respectively a set o...

Solution for the Heat Equation

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The 1-D Heat Equation

Rate of heat transfer ∂u = (1) −K0 area ∂x where K0 is the thermal conductivity, units [K0] = MLT U . In other words, heat is transferred from areas of high temp to low temp. 3. Conservation of energy. Consider a uniform rod of length l with non-uniform temperature lying on the x-axis from x = 0 to x = l. By uniform rod, we mean the density ρ, specific heat c, thermal conductivity K0, cross-sec...

Solution of Systems of Polynomial Equation by Using Bernstein Expansion