-- abc.adb  User problem definitions for a specific PDE to be solved
--          this includes the user choice of degree and discretization
--
--          The problem must be well posed and the solution must be
--          continuous and continuously differentiable
--
-- The general PDE to be solved is:
--  a1(x,y)*uxx(x,y) + b1(x,y)*uxy(x,y) + c1(x,y)*uyy(x,y) +
--  d1(x,y)*ux(x,y) + e1(x,y)*uy(x,y) + f1(x,y)*u(x,y) = c(x,y)
--
with Real_Arrays; -- type Real comes from here
use  Real_Arrays;
with Ada.Numerics.Long_Elementary_Functions;
use  Ada.Numerics.Long_Elementary_Functions;

package body abc is
-- the user must provide all functions, even if only  return 0.0;
-- the functions are implemented in the file  abc.abd
-- A specific set of test functions is covered in abc.txt

function a1(x:Real; y:Real) return Real is
begin
  return exp(x/2.0)*exp(y)/2.0;
end a1;

function b1(x:Real; y:Real) return Real is
begin
  return 0.7/(x*x*y*y+0.5);
end b1;

function c1(x:Real; y:Real) return Real is
begin
  return (4.0 - exp(x) - exp(y/2.0))*2.0;
end c1;

function d1(x:Real; y:Real) return Real is
begin
  return x*x+y;
end d1;

function e1(x:Real; y:Real) return Real is
begin
  return x*y*y;
end e1;

function f1(x:Real; y:Real) return Real is
begin
  return 3.0*x + 2.0*y;
end f1;

function u (x:Real; y:Real) return Real is
begin      -- must compute boundary, if solution, then set ifcheck := 1
  return x*x*x + 2.0*y*y*y + 3.0*x*x*y + 4.0*x*y*y + 5.0*x*y +
    6.0*x + 7.0*y + 8.0;
end u;

function c (x:Real; y:Real) return Real is  -- this becomes defined by a1...f1
begin
  return 0.5*exp(x/2.0)*exp(y)*(6.0*x+6.0*y)             +
    0.7*(6.0*x + 8.0*y + 5.0)/(x*x*y*y+0.5)              +
    (8.0 - 2.0*exp(x) - 2.0*exp(y/2.0))*(12.0*y + 8.0*x) +
    (x*x+y)*(3.0*x*x + 6.0*x*y + 4.0*y*y + 5.0*y + 6.0)  +
    x*y*y*(6.0*y*y + 3.0*x*x + 8.0*x*y + 5.0*x +7.0)     +
    (3.0*x + 2.0*Y)*(x*x*x + 2.0*y*y*y + 3.0*x*x*y + 4.0*x*y*y + 5.0*x*y +
    6.0*x + 7.0*y + 8.0);
end c;

end abc;