Abstract
We establish the conditions for the compute of the Global Truncation Error (GTE), stability restriction on the time step and we prove the consistency using forward Euler in time and a fourth order discretization in space for Heat Equation with smooth initial conditions and Dirichlet boundary conditions.
Highlights
In this paper we have considered the heat equation ut = Cuxx on [0,1]×[0,T ] with smooth initial conditions
Using forward Euler in time and fourth order discretization in space, we compute the Global Truncation Error (GTE), the stability restriction on the time step ∆t, we prove consistency and we prove the convergence for this scheme
Many problems are modeled by smooth initial conditions and Dirichlet boundary conditions
Summary
In this paper we have considered the heat equation ut = Cuxx on [0,1]×[0,T ] with smooth initial conditions ( ) and Dirichlet boundary conditions C ∈ +. Using forward Euler in time and fourth order discretization in space, we compute the Global Truncation Error (GTE), the stability restriction on the time step ∆t , we prove consistency and we prove the convergence for this scheme. (2014) A Survey of the Implementation of Numerical Schemes for the Heat Equation Using Forward Euler in Time. Cárdenas Alzate discretization from the previous problem in space, the heat equation reads: uin+1 − uin = C −uin−2 + 16uin−1 − 30uin + 16uin+1 − uin+2. We can compute the one-step-error for the scheme. We can estimate the GTE by summing up the one-step error at each stage ( ) N
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