14-point method.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(integration_class_1d), | intent(inout) | :: | me | |||
| real(kind=wp), | intent(in) | :: | x | |||
| real(kind=wp), | intent(in) | :: | h |
function g14(me, x, h) result(f)
implicit none
class(integration_class_1d),intent(inout) :: me
real(wp), intent(in) :: x
real(wp), intent(in) :: h
real(wp) :: f
!> abscissae:
real(wp),dimension(7),parameter :: a = [ 0.10805494870734366206624465021983474761195160547&
&4237557040821061308013529011730007130100688176689&
&3672374502026424466474638099232632258191427567218&
&1973150409752806137273842265069487944308775321508&
&8445556391329819060204836416480024319739665907101&
&2506161702814425014635643221773541001328892761_wp,&
&0.31911236892788976043567182416847546683426120353&
&3843956596650187257333440512792783164933705421346&
&4131802793151826090394496145640578710017716508863&
&2222396245608012120993128542172348808287716458637&
&8479374239121304478425121768114783511643536777896&
&2949997448460558214759676525644841351801594858_wp,&
&0.51524863635815409196529071855118866230888528256&
&9306036951504769092784951832055660452072020350772&
&8923922907932905090138695274035571340047593918260&
&5653057211011637652073200342580823038532041784020&
&3436173906624491224801618641571038235567674745455&
&3979637438627635490786064892912451481973721288_wp,&
&0.68729290481168547014801980301933413753840121274&
&7170675619266488628184896183133256947373070505211&
&8384106603630216790054729627432715418501010682124&
&6881727389082952662885443589912839338608106959371&
&4595904926885388784713769175169784875289055161406&
&7877996475717650653147982694804026342351254071_wp,&
&0.82720131506976499318979474265039496103970110147&
&5081181560709054241479830810028873570426390137889&
&5453991241406273986535333275661226737816179582645&
&1069907936808669317564778014567859855078251147291&
&5830426696849656086721489336979443959282673643228&
&6425172143208924251106624044295037127737490111_wp,&
&0.92843488366357351733639113937787426447703921040&
&9837618717962447482131093544359853111413905683657&
&5176363551261559882603607008578010786539258018984&
&5400440650494157888098179531161147719130825235345&
&8596605653673043686690855550898698329741248613224&
&5749388483890945436457404705549484348178721002_wp,&
&0.98628380869681233884159726670405280167609140723&
&9225881644070811777749554132491637910646239665151&
&7527602612562941358578689852603067447974494119727&
&0324710898207170072955675048180261687970555989447&
&5396929426197069500447181272675429908986256542893&
&3676463914802477677291745002965827767360741735_wp ]
!> weights:
real(wp),dimension(7),parameter :: w = [ 0.21526385346315779019587644331626003527499755805&
&4128800219776392543618787353994604001024441410819&
&5782372566723324367709929481659764649301890356019&
&0805098142804175780269156508228762641736544919294&
&6281203662033345376460522564310634412912654698349&
&487266562730897512393716549425155133887783267_wp,&
&0.20519846372129560396592406566121805571033906130&
&9419451716897290283367144825249720339431839991890&
&8957243692694424494287284534856133850644865918702&
&3021403166714178733299347482783913811132568481282&
&5439676020905052976535424973123755325146919285189&
&8072394707049964721031773292256965337005468577_wp,&
&0.18553839747793781374171659012515703624892260293&
&7331659020034925069098350263525444425552731146712&
&2229825611215057289188990778964974252160895085525&
&2415283643607286404060027232379697141385075345609&
&3331227890449938852384485366393922617921879824760&
&6150274514935557012909889503067356410067833406_wp,&
&0.15720316715819353456960193862384215660566803733&
&7323374969317043874768176369608298513958093362418&
&0762768531519990811885018854374920646576267489242&
&9103726460198700102219564745910784232280561068611&
&6907713218466935160138377442838502265889923868443&
&9084685022864905124096570215866733146092008329_wp,&
&0.12151857068790318468941480907247662595666934569&
&0074672291075392543159743892526492318819906270375&
&0071489155506530592569942811574313408868548096421&
&2571445460802891854106154207862005646754562932960&
&2540610239636717985405900755004972904989241013019&
&1072357341821083329663867464821867539341968434_wp,&
&0.08015808715976020980563327706285430958369778539&
&4594765201399065489571474457287169863536190819137&
&7559686225015908038847487953091382572604434376755&
&1198447409477973877237005366105771785226539545491&
&2313554662497115946457665357652160093748935412771&
&0937535198838649279475628473516378736712929573_wp,&
&0.03511946033175186303183287613819178061970560927&
&7127276581499890196416322837808270537676796998646&
&4636614217324764405511345585478510619843098677334&
&0884595716394793248808744456729064741484147706750&
&3186014306010893702617623540676052379390445897465&
&9810087587180865408885105556219147609526200925_wp ]
f = h * ( w(1)*( me%fun(x-a(1)*h) + me%fun(x+a(1)*h) ) + &
w(2)*( me%fun(x-a(2)*h) + me%fun(x+a(2)*h) ) + &
w(3)*( me%fun(x-a(3)*h) + me%fun(x+a(3)*h) ) + &
w(4)*( me%fun(x-a(4)*h) + me%fun(x+a(4)*h) ) + &
w(5)*( me%fun(x-a(5)*h) + me%fun(x+a(5)*h) ) + &
w(6)*( me%fun(x-a(6)*h) + me%fun(x+a(6)*h) ) + &
w(7)*( me%fun(x-a(7)*h) + me%fun(x+a(7)*h) ) )
end function g14