A Discussion on Numerical Analysis of Partial Differential EquationsJames Hardy Wilkinson |
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Page 157
... mesh of side h with the boundaries along mesh - lines . Suppose the internal mesh - points are numbered consecutively along rows , and there are m mesh - points in each row . Then to repre- sent the differential equation at the point i , we ...
... mesh of side h with the boundaries along mesh - lines . Suppose the internal mesh - points are numbered consecutively along rows , and there are m mesh - points in each row . Then to repre- sent the differential equation at the point i , we ...
Page 172
... mesh - points in our extrapolation procedures , we have to conclude that Richardson extrapolation cannot be expected always to succeed . A remedy is suggested by the use of a more accurate approximation at boundary mesh - points which ...
... mesh - points in our extrapolation procedures , we have to conclude that Richardson extrapolation cannot be expected always to succeed . A remedy is suggested by the use of a more accurate approximation at boundary mesh - points which ...
Page 192
... mesh - points x = ah , where a = ( α1 , ... , αa ) is a multi - integer . We shall consider finite - difference ... mesh - points x , N be the convex hull of the set { x + ẞh , bg + 0 } . Then x is said to be an interior mesh - point ...
... mesh - points x = ah , where a = ( α1 , ... , αa ) is a multi - integer . We shall consider finite - difference ... mesh - points x , N be the convex hull of the set { x + ẞh , bg + 0 } . Then x is said to be an interior mesh - point ...
Contents
A DISCUSSION ON NUMERICAL ANALYSIS OF PARTIAL | 153 |
O B WIDLUND | 167 |
L | 179 |
11 other sections not shown
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accuracy accurate algorithms analysis applied approach approximation assume become bound boundary conditions boundary-value problems calculation characteristic coefficients Comput conservation consider considerably constant construct continuous convergence corresponding defined dependent derivatives described determined developed difference scheme difficulties dimensions direction discrete discussed elliptic energy error estimate example exists expansion figure finite finite-difference flow formula function give given grid important inequality initial instability integral equation interpolation introduce involving length limit linear Math mean mesh mesh-points method necessary nonlinear norm numerical numerical solution obtained operator partial differential equations particular physical points positive possible practical present problem procedure properties recent reduced REFERENCES region relations requires respectively satisfy shown similar simple singularities smooth solution solving space spline stability step sufficient techniques THEOREM unique values variables wave дх