Notes in Numerical solution of PDEs

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Status	Last Update	Fields
Published	05/06/2024	State the trapezoidal (Crank-Nicolson) method
Published	05/06/2024	When is a function \(f(h)\) said to be \(O(h^n)\) for small \(h\)?
Published	05/06/2024	How are the points \(x_{j}\) chosen?
Published	05/06/2024	What is the formula for the grid spacing between points?
Published	05/06/2024	State taylor's theorem
Published	05/06/2024	State the forward difference approximation method
Published	05/06/2024	When is a finite-difference method said to be an nth order approximation?
Published	05/06/2024	What does the remainder term describe?
Published	05/06/2024	State the centered differencing appproximation
Published	05/06/2024	What is the explicit (forward) euler method?
Published	05/06/2024	Name an example of a time stepping method?
Published	05/06/2024	State the implicit (backward) Euler method
Published	05/06/2024	State the \(\theta\) method
Published	05/06/2024	What does the finite difference method do?
Published	05/06/2024	What is global error?
Published	05/15/2024	When is a finite-difference method said to be convergent?
Published	05/06/2024	What is the local truncation error \(T_j\) at the grid point \(x_j\)?
Published	05/06/2024	When is a finite-difference method said to be k-th order consistent for \(k>0\)?
Published	05/06/2024	What order of consistency do forward and backward finite-difference approximations of the first spatial derivative have?
Published	05/06/2024	What order of consistency do the central difference approximations of the first and second spatial derivatives have?
Published	05/06/2024	When is a finite-difference method convergent?
Published	05/06/2024	When is a numerical method stable?
Published	05/06/2024	How is the region of absolute stability defined for a given finite difference scheme?
Published	05/06/2024	What is the mesh-Peclet number?
Published	05/06/2024	When is the centre difference approximation stable?
Published	05/06/2024	State the stability theorem for finite-differene schemes for BVPs
Status	Last Update	Fields