Question

solve the Laplace equation uxx+uyy=0, 0<x<1,0<y<1,given u(x,1)=u(0,y)=0,u(x,0)=9(x-x²),u(1,y)=9(y-y²) take h=1/3​

Answer 1

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• Mathematics is the science that deals with the logic of shape, quantity and arrangement. Math is all around us, in everything we do. It is the building block for everything in our daily lives, including mobile devices, architecture (ancient and modern), art, money, engineering, and even sports.

Answer 2

Step-by-step explanation:

The sum on the left often is represented by the expression ∇2R, in which the symbol ∇2 is called the Laplacian, or the Laplace operator.

A function 0si which satisfies Laplace's equation is said to be harmonic. A solution to Laplace's equation has the property that the average value over a spherical surface is equal to the value at the center of the sphere.

A solution to Laplace's equation is uniquely determined if

• The value of the function is specified on all boundaries

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• The normal derivative of the function is specified on all boundaries