Numerical Computation For A Class Of Heat Equation With Nonlinear Boundary Condition

Heat conduction equations are often arised from problems in solid dynamics and engineering. The difference schemes and numerical computation for solving these equations are discussed in the thesis. By Taylor expansions, we derive a difference method having o(h2+Ï„2) order inside the domain and o(Ï„2) order on the boundary. The theoretical analysis is set on another difference system which is equivalent to the difference method we established. We obtain the error estimates and the convergence theorem of the difference scheme. In addition, we have gradually proven and obtained the existence and the uniqueness of the difference solution by making use of a theorem with respect to fixed point. Finally, the nonlinear boundary condition is analyzed by giving several different nonlinear functions G(t, u)'s which satisfy the conditions. The final part of the thesis is devoted to the comparison with many numerical examples. Numerical results show that our schemes for the heat equations are efficient.