diff --git a/pdeSolver.c b/pdeSolver.c index c23fca311adc569defc0a6f491ace6b8bfe2a6b4..fb9c4ead83d4117b7e6f56cfc6ffcda214d21771 100644 --- a/pdeSolver.c +++ b/pdeSolver.c @@ -260,4 +260,48 @@ int main(int argc, char *argv[]) { // Nx columns and Ny rows. return 0; -} \ No newline at end of file +} + +/* +u(i,j) = f(x,y) + (u(i+1,j) + u(i-1,j))/Δx² + (u(i,j+1) + u(i,j-1))/Δy² + (-u(i+1,j)+u(i-1,j))/2Δx + (-u(i,j+1)+u(i,j-1))/2Δy + -------------------------------------------------------------------------------------------------------------------- + 2/Δx² + 2/Δy² + 4π² + + +Formato: + +Ax = B + +A [a11 a12 a13] * X [x1] = B [b1] -> a11*x1 + a12*x2 + a13*x3 = b1 -> x1 = (b1 - a12*x2 - a13*x3)/a11 + [a21 a22 a23] [x2] [b2] -> a11*x1 + a12*x2 + a13*x3 = b2 -> x2 = (b2 - a11*x1 - a13*x3)/a12 + [a31 a32 a33] [x3] [b3] -> a11*x1 + a12*x2 + a13*x3 = b3 -> x3 = (b3 - a11*x1 - a12*x2)/a13 + +se x1 = u(1,1), sei calcular x1 da forma double u(int i, int j) {} +Mesmo vale pra x2 e x3. E valeria pra x4, x5, x6, etc. + + +Se u for uma matriz de 6 elementos. Ou seja, Hx = 0.25 e Hy = 0.3 + +u u u u +u x5 x6 u +u x3 x4 u +u x1 x2 u +u u u u + +5 linhas, 4 colunas. +Ny = 3, Nx = 2. + +x1 = u11 +x2 = u12 +x3 = u13 +x4 = u21 +x5 = u22 +x6 = u23 + +Matriz A, olhando pela equação u(i,j) obtida, seria algo assim: +A = [1 ] + [ 1 ] + [ 1 ] + [ 1 ] + [ 1] +*/