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3409Boundary Curvature Under Zero FluxSuppose u(0)=7, u 1=6, h=0.5, and the left boundary has zero flux. What second derivative estimate follows from the ghost-point stencil (u -1 -2u 0+u 1)/h 2?数学中等derivation未尝试面试订阅3410Second-Order Forward Stencil at a BoundaryUse the second-order forward stencil (-3f(0)+4f(h)-f(2h))/(2h) with h=0.1, f(0)=1, f(0.1)=1.24, and f(0.2)=1.52. What derivative estimate do you get at 0?数学中等derivation未尝试面试订阅3411Why Richardson Extrapolation HelpsWhy does Richardson extrapolation often improve an estimate even when you never see the exact derivative value?数学中等essay未尝试面试订阅3412Why Smaller h Is Not Always BetterWhy can making h smaller eventually worsen a finite-difference estimate?数学中等essay未尝试面试订阅3413Why Diffusion Stability Scales With Delta x SquaredWhy does the explicit heat-equation time-step restriction shrink like Delta x squared rather than just like Delta x?数学中等essay未尝试面试订阅3414Why Boundary Conditions Change the StencilWhy can the same derivative operator require a different finite-difference stencil near a boundary than in the interior?数学中等essay未尝试面试订阅3415Why Central Differences Are Usually More Accurate Than One-Sided OnesWhy do central differences often achieve a higher order of accuracy than one-sided differences using similar nearby points?数学中等essay未尝试面试订阅