A Discussion on Numerical Analysis of Partial Differential EquationsJames Hardy Wilkinson |
From inside the book
Results 1-3 of 30
Page 174
... assume further that the maximum norm || u || ∞ , h sup u ( x ) , x on the mesh , and that the norm || . || is related by an inequality of the form h || u || ∞ , const . × h − 9 || u || n И = for all mesh functions u . Such a relation ...
... assume further that the maximum norm || u || ∞ , h sup u ( x ) , x on the mesh , and that the norm || . || is related by an inequality of the form h || u || ∞ , const . × h − 9 || u || n И = for all mesh functions u . Such a relation ...
Page 194
... assume that the operator L is in divergence form , d Ә Lu = Σ ди Азкахк 1. 11 dx ( ask a j , k = 1 We shall be concerned with some difference operators L which are particularly simple in that they only contain neighbours of x which are ...
... assume that the operator L is in divergence form , d Ә Lu = Σ ди Азкахк 1. 11 dx ( ask a j , k = 1 We shall be concerned with some difference operators L which are particularly simple in that they only contain neighbours of x which are ...
Page 199
... Assume that Q approximates the differential operator Q with accuracy μ ( μ = 1 or 2 ) and let R1 and R2 be as above . Then if u and u are solutions of ( 5.1 ) and ( 5.2 ) , respectively , and u is sufficiently smooth we have | QnUn− Qu ...
... Assume that Q approximates the differential operator Q with accuracy μ ( μ = 1 or 2 ) and let R1 and R2 be as above . Then if u and u are solutions of ( 5.1 ) and ( 5.2 ) , respectively , and u is sufficiently smooth we have | QnUn− Qu ...
Contents
A DISCUSSION ON NUMERICAL ANALYSIS OF PARTIAL | 153 |
O B WIDLUND | 167 |
L | 179 |
11 other sections not shown
Common terms and phrases
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