High-order finite-difference methods for Poisson’s equation
High-order finite-difference methods for Poisson’s equation
Finite-difference approximations to the three boundary value problems for Poisson’s equation are given with discretization errors of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper O left-parenthesis h cubed right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>h</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">O({h^3})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for the mixed …