THE METHOD OF LINES FOR NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS
ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
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In the method of lines for solving certain kinds of boundary value problems in rectangular or trapezoidal regions one of the variables, say y, is discretized while the other variable x is left continuous. When suitable finite difference approximations are substituted for the partial derivatives with respect to y the differential equation is changed into a simultaneous system of ordinary differential equations in the variable x. The method used very little in the USA is used extensively in the Soviet Union and nearly all the literature on this subject is in Russian. The method has been tried in BRL and it seems to be a very useful one. This report does not pretend to be a monograph on the subject. It intends to be a practical guide to computations.
- Numerical Mathematics