function?res?=?ENO4_L（wfluxdfluxSdx）
%%?Lax-Friedrichs?通量分裂，u是左值，v是右值
a=max（abs（dflux（w）））;?v0=0.5*（flux（w）+a*w）;?u0=circshift（0.5*（flux（w）-a*w）[0-1]）;

%%?Right?Flux
hn?=?v_reconstructe（v0）;
hp?=?fliplr（v_reconstructe（fliplr（u0）））;
res?=?（hp-circshift（hp[01]）+hn-circshift（hn[01]））/dx?-?S（w）;
end
function?hn?=?v_reconstructe（v0）
v?=?[v0（end-2:end）?v0?v0（1:3）];%前后擴充
n?=?length（v）;k?=?4;m?=?k-1;
DQ_table?=?zeros（n4）;
DQ_table（:1）?=?v;
for?i=2:4
????current_col?=?DQ_table（:i-1）;
????DQ_table（1:end-i+1i）?=?current_col（2:end-i+2）?-?current_col（1:end-1-i+2）;
end
IS?=?1:n;
abs_DQ?=?abs（DQ_table）;
for?i?=?4:n-3
for?j?=?2:m+1
????if（abs_DQ（IS（i）-1j）????????IS（i）?=?IS（i）?-?1;
????end
end
end
Crj?=?[1/4?13/12?-5/12?1/12;
????-1/12?7/12?7/12?-1/12;
????1/12?-5/12?13/12?1/4;
????-1/4?13/12?-23/12?25/12;
????];

hn?=?zeros（）;
for?i?=?4:n-3
????r?=?i?-?IS（i）;
????row_ind?=?r?+?1;
????hn（i-3）?=?dot（Crj（row_ind:）v（IS（i）:IS（i）+k-1））;
end
end





%?vmmm?=?circshift（v[0?3]）;
%?vmm?=?circshift（v[0?2]）;
%?vm??=?circshift（v[0?1]）;
%?vp??=?circshift（v[0?-1]）;
%?vpp?=?circshift（v[0?-2]）;
%?vppp?=?circshift（v[0?-3]）;
%?
%?IS?=?1:len;%模板起始下標
%?for?i?=?1:len
%?????
%?end
%?
%?
%?%?多項式重構右值
%?p0n?=?（2*vmm?-?7*vm?+?11*v）/6;%i-2+0為起始的模板
%?p1n?=?（?-vm??+?5*v??+?2*vp）/6;%i-2+1為起始的模板
%?p2n?=?（2*v???+?5*vp?-?vpp?）/6;%i-2+2為起始的模板
%?
%?%?Smooth?Indicators?（Beta?factors）
%?%syms?vmm?vm?v?vp?vpp
%?B0n?=?13/12*（vmm-2*vm+v??）.^2?+?1/4*（vmm-4*vm+3*v）.^2;?
%?B1n?=?13/12*（vm?-2*v?+vp?）.^2?+?1/4*（vm-vp）.^2;
%?B2n?=?13/12*（v??-2*vp+vpp）.^2?+?1/4*（3*v-4*vp+vpp）.^2;
%?
%?%?Constants
%?d0n?=?1/10;?d1n?=?6/10;?d2n?=?3/10;?epsilon?=?1e-6;
%?
%?%?Alpha?weights?
%?alpha0n?=?d0n./（epsilon?+?B0n）.^2;
%?alpha1n?=?d1n./（epsilon?+?B1n）.^2;
%?alpha2n?=?d2n./（epsilon?+?B2n）.^2;
%?alphasumn?=?alpha0n?+?alpha1n?+?alpha2n;
%?
%?%?ENO?stencils?weigths
%?w0n?=?alpha0n./alphasumn;
%?w1n?=?alpha1n./alphasumn;
%?w2n?=?alpha2n./alphasumn;
%?
%?%?Numerical?Flux?at?cell?boundary?$u_{i+1/2}^{-}$;
%?hn?=?w0n.*p0n?+?w1n.*p1n?+?w2n.*p2n;

%%?Left?Flux?
%?Choose?the?negative?fluxes?‘u‘?to?compute?the?left?cell?boundary?flux:
%?$u_{i-1/2}^{+}$?

%?umm?=?circshift（u[0?2]）;%m為-，p為+
%?um??=?circshift（u[0?1]）;
%?up??=?circshift（u[0?-1]）;
%?upp?=?circshift（u[0?-2]）;
%?
%?%?Polynomials
%?p0p?=?（?-umm?+?5*um?+?2*u??）/6;
%?p1p?=?（?2*um?+?5*u??-?up???）/6;
%?p2p?=?（11*u??-?7*up?+?2*upp）/6;
%?
%?%?Smooth?Indicators?（Beta?factors）
%?B0p?=?13/12*（umm-2*um+u??）.^2?+?1/4*（umm-4*um+3*u）.^2;?
%?B1p?=?13/12*（um?-2*u?+up?）.^2?+?1/4*（um-up）.^2;
%?B2p?=?13/12*（u??-2*up+upp）.^2?+?1/4*（3*u?-4*up+upp）.^2;
%?
%?%?Constants
%?d0p?=?3/10;?d1p?=?6/10;?d2p?=?1/10;?epsilon?=?1e-6;
%?
%?%?Alpha?weights?
%?alpha0p?=?d0p./（epsilon?+?B0p）.^2;
%?alpha1p?=?d1p./（epsilon?+?B1p）.^2;
%?alpha2p?=?d2p./（epsilon?+?B2p）.^2;
%?alphasump?=?alpha0p?+?alpha1p?+?alpha2p;
%?
%?%?ENO?stencils?weigths
%?w0p?=?al

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????3275??2018-01-15?17:50??ENO4_L.m
?????文件?????????590??2018-01-15?10:31??ExSolu.m
?????文件?????????217??2018-01-15?22:11??ExSolu_Refine.m
?????文件???????15218??2018-01-15?21:56??ExSoluDatau.mat
?????文件????????1829??2018-01-15?16:26??gif動圖繪制.m
?????文件????????3149??2018-01-15?22:27??Proj3main.m
?????文件????????1231??2018-01-15?14:14??WENO3_L.m
?????文件????????1936??2018-01-15?14:46??WENO5_L.m