62 lines
2.1 KiB
Chapel
62 lines
2.1 KiB
Chapel
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module LinearMultiStep {
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record empty {}
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record cons {
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param weight;
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type tail;
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}
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proc initial(type x : empty) param return 0;
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proc initial(type x : cons(?w, ?t)) param return 1 + initial(t);
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proc cff(param x : int, type ct : cons(?w, ?t)) param {
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if x == 1 {
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return w;
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} else {
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return cff(x-1, t);
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}
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}
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proc runMethod(type method, step : real, count : int, start : real,
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n : real ... initial(method)): real {
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param coeffCount = initial(method);
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// Repeat the methods as many times as requested
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for i in 1..count {
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// We're computing by adding h*b_j*f(...) to y_n.
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// Set total to y_n.
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var total = n(coeffCount - 1);
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for param j in 1..coeffCount do
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// For each coefficient b_j given by cff(j, method)
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// increment the total by h*bj*f(...)
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total += step * cff(j, method) *
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f(start + step*(i-1+coeffCount-j), n(coeffCount-j));
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// Shift each y_i over by one, and set y_{n+s} to the
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// newly computed total.
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for j in 0..< coeffCount - 1 do
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n(j) = n(j+1);
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n(coeffCount - 1) = total;
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}
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// return final y_{n+s}
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return n(coeffCount - 1);
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}
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}
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proc f(t: real, y: real) return y;
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use LinearMultiStep;
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type euler = cons(1.0, empty);
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type adamsBashforth = cons(3.0/2.0, cons(-0.5, empty));
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type someThirdMethod = cons(23.0/12.0, cons(-16.0/12.0, cons(5.0/12.0, empty)));
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// prints 5.0625 (correct)
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writeln(runMethod(euler, step=0.5, count=4, start=0, 1));
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// For Adams-Bashforth, pick second initial point from Euler's method
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// returns 6.0234 (correct)
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writeln(runMethod(adamsBashforth, step=0.5, count=3, start=0, 1,
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runMethod(euler, step=0.5, count=1, start=0, 1)));
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writeln(runMethod(someThirdMethod, step=0.5, count=2, start=0,
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1,
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runMethod(euler, step=0.5, count=1, start=0, 1),
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runMethod(adamsBashforth, step=0.5, count=1, start=0, 1, runMethod(euler, step=0.5, count=1, start=0, 1))));
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